How do Calvinists go from "X is Sinful" to "X is unable to accept Christ on his own?"

I am not sure I see "sin" as even part of the equation.

John 6:44 No man can come to me, except the Father which hath sent me draw him: and I will raise him up at the last day.

It seems pretty straightforward. No one can come to Jesus without the work of the Father.

X -> work of the Father -> belief in Christ

I think your problem comes in your understanding of the statement, "X is sinful". In context, when a Calvinist says "Fred Jones is sinful", he does not simply mean, "Fred Jones has committed many sins". What he means is more like, "Fred Jones mind is totally controlled by sin."

It's like if I said, "X is wet -> X will never be dry without radical intervention". If when you read "X is wet" you think of something that has been left out in the rain, the logic doesn't follow. Why can't I bring it inside and dry it out? Won't it dry out when the sun comes out? Etc. But if the person who said "X is wet" was thinking of a fish that lives at the bottom of the ocean, then the logic makes perfect sense.

When the Calvinist says that people are sinners, he is thinking of the relationship of a human to sin as like a fish to the ocean, not a rag to the rain.

You have it right: "X is sinful" -> "everything X does is sin" -> "X is incapable of believing in Christ without the additional work of the Holy Spirit" --> is the basic belief held by Calvinism. One of the best explanations of the doctrine of original sin is by Jonathan Edwards, entitled ‘without surprise’, ‘The Great Christian Doctrine of Original Sin Defended; Evidences of its Truth Produced.’ Here he argues, among other things, the imputation of guilt on infants as displayed in the flood and in Sodom and Gomorrah.

In a nutshell I have found many classic authors, including Luther, Owen and Edwards, often start by using this verse to say that anybody born of ‘flesh’ is only ‘flesh’.

That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. (ESV John 3:6)

In other words anyone born in the sinful nature is in ‘entirely sinful.’ This means they can’t do anything good but are totally depraved.

The idea of ‘flesh’ is derogatory as ‘human nature separated from God’. Even as a believer who has ‘both’ good and evil natures, as a result of the new birth, only a sinful disposition remains in that nature they first obtained through Adam.

For I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out. (ESV Romans 7:18)

This is understood by all classical Calvinists (as far as I know) as a description of Paul ‘as a Christian’.

Edwards’ book which I referenced argues the case so very well. Unlike Owen who is difficult to read, I challenge anyone to read ‘even just a dozen pages’ of Edwards and they will quickly understand the concepts of original sin as 'originally taught' by the reformers.

A. "X is sinful" -> "everything X does is sin" -> 
     "X is incapable of believing in Christ" or

B. "X is sinful" , "no one with sin can accept Christ" -> 
      "X is incapable of believing in Christ"

Neither (A) nor (B) are acceptable terminal points in Calvinistic theology. These are not doctrines that are taught, but rather ones that you have probably either misunderstood or else that someone else has misunderstood and passed on to you.

The distinction between Reformed belief and what you mention is the difference between what R.C. Sproul calls Utter Depravity vs. Radical Corruption. It's not just that we're sinners and so therefore we cannot receive Christ (although the Holiness of God does make this true), it's that our wills are bound by sin so that we have no desire whatsoever to focus on the things of God and to be saved.

I'll filter out Piper's verses to show the most pertinent ones:

We see that the mind set not on things of the spirit is not capable of being subject to the Law of God.

Romans 8:5-9 For those who are according to the flesh set their minds on the things of the flesh, but those who are according to the Spirit, the things of the Spirit. For the mind set on the flesh is death, but the mind set on the Spirit is life and peace, because the mind set on the flesh is hostile toward God; for it does not subject itself to the law of God, for it is not even able to do so, and those who are in the flesh cannot please God. However, you are not in the flesh but in the Spirit, if indeed the Spirit of God dwells in you. But if anyone does not have the Spirit of Christ, he does not belong to Him.

This is our natural state.

Ephesians 2:1-5 And you were dead in your trespasses and sins, in which you formerly walked according to the course of this world, according to the prince of the power of the air, of the spirit that is now working in the sons of disobedience. Among them we too all formerly lived in the lusts of our flesh, indulging the desires of the flesh and of the mind, and were by nature children of wrath, even as the rest.

You asked what the "middle point" was so that we come to receive Christ, even though we are incapable. The answer lies in the end of the Ephesians passage cited. God made us alive.

But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved).

The other verses he lists summarize it quite well and offer more support, but these two are probably the crux of the matter.