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.