From 1936-45 what was the prescribed punishment in Nazi Germany for failing to join or participate in the Hitler Youth?

Membership and service were obligatory. True, on paper. But especially those who joined by decree from an older, now abolished organisation were sometimes less enthusiastic about actually showing up for service, meetings etc.

Parents dissuading their children had not much to fear, in reality, despite the laws and actions. It became a problem for parents in mainly two cases: They prohibited it but the kids were already eager to join. That would incur a visit from a official that the 'persuaded' the parents otherwise. 2. If the kids got in trouble and were not members of the HJ. But then mainly for the trouble not for membership parents could suffer Sippenhaft. This violation of German grammar means that an arbitrary number of relatives were punished for the deeds of one family member.
As soon as a village showed a majority support for opposing the HJ the Nazi officials usually gave up. In Landsberg there were just no HJ service days for up to three years during the war. The majority there thought that youth better go to church than a HJ drill.

One example for just never joining would be Joachim Clemens Fest, one of Hitlers later biographers.

The nearly complete arbitrariness of persecutions and punishments was one defining aspect. The propagandistic assertion that membership was complete, and complete because of that, is still a myth.

There were even quite a number of organised resistance movements among youths. Sadly, those were seen as un-German, really a shaming reminder to all those who did join the Nazis that resistance was possible, and the survivors of those groups were marginalised for being not Nazi enough, long after the war (until at least the 1980s).

First, we need to concede that enforcement and sanctions grew ever tougher over time. But it needs reminding that persecution of this kind of deviancy was essentially quite arbitrary. But chances were not that low to get away with not even joining in the first place.

Three institutions were mainly employed for enforcement: the Hitler Youth itself (directing the force against its own members, with limited success). While within the HJ from social pressure to penal service the range was quite limited. The ultimate punishment from the HJ within the HJ was expulsion.
The second agency was the judiciary. This could reach beyond Hitler Youth membership. But it was still somewhat 'hampered' in the early years by a comparatively humane legal heritage from the Weimar Republic. The judiciary sharpened its approach to wayward youth only under constant pressure from the police and SS, both of which attempted to neutralise it entirely.
The third agency was Himmler’s police with all its branches. This police viewed itself as extra-legal and supreme and would become ever more successful with each passing year of the war. They 'visited' homes, beat up the young, arrested them, or send them off to camps.

Disciplinary procedures in place for the Hitler Youth could be invoked whenever any of the aberrant youths were members and proved to have absented themselves from HJ service. Hence in early March 1940, when the Swing celebrations in the Hamburg Curio-Haus were uncovered, 102 of the male suspects indicted actually were HJ members, of a total of 237 culprits; 52 had left the HJ and 58 had never joined.
Since the lines between HJ membership and non-membership were often blurred, the Hitler Youth frequently erred on the side of injustice simply to go after its quarry successfully. In the case of Hamburg’s “Tommie” Scheel, who was a Hitler Youth turned Swing and who at seventeen was grabbed by the Gestapo in 1940, even his school teachers could not say whether he was in the HJ or not.

The HJ employed its own 'police on foot' the SRD to roam the streets and look for delinquents. That is members behaving badly, or non-members! Since the SRD did not carry weapons for that task, oppositional groups like Meuten or Edelweisspiraten could get away, even deal the SRDs quite severe beatings. But the SRD could always call in the police or SS, and then…

But how weak the HJ leadership really was in suppressing disobedient youth is demonstrated by its failure to deal with the Swing Youth phenomenon when it was in full bloom. On January 8, 1942, HJ boss Axmann directed the following message to Himmler, as chief of the police forces, Gestapo, and SS: “In the upper schools of Hamburg or in the young affluent merchant class a so-called ‘Swing Youth’ has developed, which largely displays an Anglophile proclivity … Since the activities of this ‘Swing Youth’ at the home front cause a reduction in German national capacities, I think it essential that these people be immediately taken to a work camp … I would very much appreciate an order to your Hamburg offices to the effect that the ‘Swing Youth’ will be proceeded against as severely as possible.”

Himmler subsequently employed the concentration camp system against dissident adolescents in Nazi Germany in such a harsh manner that Axmann, shortly before his death in 1996, regretted ever having alerted the police chief.

Although the judiciary eventually surrendered much of its power to the police executive authorities, thereby severely afflicting German youth, it had been on a course of radicalization of its own since the last, authoritarian, years of the Weimar Republic. In general, this amounted to an undoing of liberal changes wrought by a reformation of the justice system under the auspices of the Weimar constitution, with the key year being 1923.

After 1941 young offenders were sent to solitary confinement, ordered to keep totally silent on a diet of bread and water. This was deemed particularly effective, as those kids were returned pretty demoralised from this torture. This was the most common punishment up to 1941, although most often just for a whole Sunday, so as they did not miss school, but could be increased at will to up to four weeks.

But the spirit of those not wanting to join could not be broken by that. After 1941 there were still the organised youth resistance movements like the above mentioned Meuten and Edelweisspiraten, and the Swingjugend:

On 18 August 1941, in a brutal police operation, over 300 Swingjugend were arrested. The measures against them ranged from cutting their hair and sending them back to school under close monitoring, to the deportation of the leaders to concentration camps. The boys went to the Moringen concentration camp while the girls were sent to Ravensbruck.

This mass arrest encouraged the youth to further their political consciousness and opposition to National Socialism. They started to distribute anti-fascist propaganda. In January 1943, Günter Discher, as one of the ringleaders of the Swing Kids, was deported to the youth concentration camp of Moringen.

On 2 January 1942, Heinrich Himmler wrote to Reinhard Heydrich calling on him to clamp down on the ringleaders of the swing movement, recommending a few years in a concentration camp with beatings and forced labor:

My judgment is that the whole evil must be radically exterminated now. I cannot but see that we have taken only half measures. All ringleaders (…) are into a concentration camp to be re-educated (…) detention in concentration camp for these youths must be longer, 2–3 years (…) it is only through the utmost brutality that we will be able to avert the dangerous spread of anglophile tendencies, in these times where Germany fights for its survival.

The crackdown soon followed: clubs were raided, and participants were hauled off to camps.

For the Edelweisspiraten, their stance of "not joining" lead to contempt from all those Nazis who did join, even long after the war. Despite the hyperbole of

According to one Nazi official in 1941, "Every child knows who the Kittelbach Pirates are. They are everywhere; there are more of them than there are Hitler Youth. They beat up the patrols… They never take no for an answer.":

Nazi response
The Nazi response to the Edelweißpiraten was relatively minor before the war, because they were viewed as a minor irritant and it didn't fit in with the policy of selective terror. As the war went on, and some 'Pirates' activities got more extreme, the punishments did too. Individuals identified by the Gestapo as belonging to the various gangs were often rounded up and released with their heads shaved to shame them. In some cases, young people were sent to concentration camps for youth or temporarily detained in prison. On October 25, 1944, Heinrich Himmler ordered a crackdown on the group and in November of that year, a group of thirteen people, the heads of the Ehrenfelder Gruppe, were publicly hanged in Cologne. Some of these were former Edelweißpiraten. The Edelweißpiraten hanged included six teenagers, amongst them Bartholomäus Schink, called Barthel, former member of the local Navajos. Fritz Theilen survived.

Nevertheless, government repression never managed to break the spirit of most groups, which constituted a subculture that rejected the norms of Nazi society. While the Edelweißpiraten assisted army deserters and others hiding from the Third Reich, they have yet to receive recognition as a resistance movement (partly because they were viewed with contempt by many of their former Youth Movement comrades, because of their 'proletarian' background and 'criminal' activities), and the families of members killed by the Nazis have as yet received no reparations.

The spectrum to observe here is quite broad, and often contradictorily colourful. Differences in refusal were seen in aspects of regional, ethical, political, class heritage or orientation. The actual absolute numbers compared to happily organised members was of course low. Just much higher than commonly described. During all of the 30s refusal was quite often possible without much consequence. The real attempt to crack down on all of those dissenters was a slowly growing process that culminated late during the war.

This answer does not contradict the other two so far. It just shows that the awful label of 'totalitarianism' in this case also occludes the fact that while most youth did join and participate regularly a wide range of dissonance, deviancy, resistance, absenteeism etc was possible and the "total" from totalitarianism less 'total' or complete as commonly thought. In absolute numbers all these acts of resistance were of course not the norm, but assuming totality in enforcement is just falling for the Nazi-propaganda, once more. Alas, the majority joined really with flying colours that they only struck long after 1945 or even way too often just 'never'.

Summary

The official stance cast into law was: "every youth has joined". In reality you did not need to even join, lest show up always if you did. This was comparatively easy in rural areas or large cities. For those just unwilling reprimands were quite low in intensity and frequency.
This is just the passivity that was already deemed illegal. On the other hand, if they were anything from between connected to groups doing 'something' to actively resisting the regime, or just alleged to do so, without any grounding in law, the whole range of terror was disposed at them: from lecturing talks, beatings, incarceration, hard labour, concentration camps for youth as well as straight to hanging.

Source, if not linked: Michael H. Kater: "Hitler Youth", Harvard University Press, Cambridge, London, 2004.

The Hitler Youth Act states:

Section Four
All regulations necessary for the execution and completion of this law will be issued by the Führer.

This is government by decree, and is how totalitarian societies work. Failure to comply would result in progressively deeper investigation until one either complied, or perhaps the authorities decide to spent their efforts elsewhere. In practice, everyone joined the Hitler Youth as soon as they started to look for employment because it was forbidden to hire any youth not a member.

Meanwhile the violators had to incur all the costs associated with non-compliance and investigation: Lawyer's fees, time off work, baby-sitting arrangements, public shaming, peer pressure from neighbours and colleagues to "smarten up", possibly sanctions or reprimands by one's employer, etc.

As stated by the Wikipedia article:

[non-members] were also the subject of frequent taunts from teachers and fellow students, and could even be refused their diploma—which made it impossible to be admitted to university. A number of employers refused to offer apprenticeships to anyone who was not a member of the Hitler Youth.