At what point after the war did Confederate money begin to attain value again?

The question, as asked, has no objective answer. The collector value of a Confederate banknote is not fixed by anything, and I doubt it is particularly consistent during any given year.

Going from the general behaviour of collectables with no intrinsic utility, the price will depend very strongly on condition, quite probably varying by a factor of ten or more between mint and well-used. Other factors will include location, keenness of the collector and skill of the seller, and variations in rarity. Since there are 72 different types of genuine Confederate banknotes, plus many collectable forgeries, rarity is likely to be the most important factor.

Finally, none of these factors are likely to be strongly linked to the face value of the notes, so even if the question was answerable, the answers would inevitably be different for different denominations.

The value of Confederate money, as a currency has not changed, since the issuer (Confederate States of America) no longer exists.

Many tall tales exist on how the currency was used after the war.

The most amusing one can be seen in episode 1 of the Beverly Hillbillies.

What is true, is that many Confederate Bonds were horded (mainly in Europe) in the vain hope that they would one day be redeemed by the United States.

However, at the close of the war the re-established Federal authorities ignored these foreign bonds, like all the other bonds of the Confederate government, or of state governments under the Confederacy.

The value of an individual Banknotes or Coins have changed based on the conditions common for collecter items

• quality, rarity, demand

CSA $1.7 billion were issued as banknotes between 1861 and 1864.

Around 23,000 gold coins (using original US die) were believed to have been minted.

10.000 as 1 and 5 dollars, 13,000 in 20 dollars coins.

So around $300,000 in gold coins as compared to $1.7 billion (0.02% in gold coins) in banknotes.

1 May 1865 (last exchange): $1200.00 to $1 in gold.

Since 99.98% of CSA currency was in banknotes, comparisons with possible confederate gold coins is really not relevant.

Sources:

• Confederate States dollar
• Economy of the Confederate States of America
• Confederate Inflation Chart

Mark Johnson answered already (correctly) that Confederate Money has no value, but individual banknotes and coins (and bonds) can have value as collectors' items. This is, however, not due to Federal Authorities IGNORING Confederate Bonds or other claims - a coin or bill is also a claim against the issuer to accept it as payment. On the contrary, they made ACTIVELY sure all who had ever helped the Confederacy with deliveries or services or payments and now held cash or bonds of any Confederate authority would NEVER see any compensation.

Therefore, they passed the 14th Amendment that says in section 4, 2nd sentence: "But neither the United States nor any State shall assume or pay any debt or obligation incurred in aid of insurrection or rebellion against the United States, or any claim for the loss or emancipation of any slave; but all such debts, obligations and claims shall be held illegal and void." That means making Confederate bonds or cash again to money that has worth would require changing the US constitution. This is relatively difficult and without broad unity in US impossible. We can conclude that no people would speculate in those instruments and would be "hoarding it all with the assumption it would one day be worth something", which was asked in the third bullet in the question.

Speculation in other old bonds does happen: After fall of the Soviet-union, I read of speculators buying bonds of Czarist Russia and demanding Russia to honor them, because Russia could otherwise not raise money at some old bond markets in Western Europe. I have not heard that this speculation was successful.