We are into what I call bible-psychology. (not biblical-psychology; that is something quite different. I refuse to use words like 'self' and 'ego' and 'sub-conscious') By bible-psychology I mean the way we work as living beings. There are several words that the Bible uses to reveal truth in these realms; spirit, soul, body, mind, heart, reins, conscience, imagination. (you will notice I don't include 'the will') The fun starts when you try to put the jig-saw together. How does the heart relate to the spirit?
The Bible uses the word 'heart' for the centre of everything. It is the centre of our survival system as human beings; it is the centre of our spiritual activity; it is the centre of the sea in Jonah. It means the 'heart' of the thing. ;-)
Man's fountain is corrupt, his heart is stone. It simply means in this sense that part of his being is utterly fixed, resolute. Jer 17, which is where I am quessing you are getting your 'incurable' from begins by describing the perennial sin of Judah, idolatry. It is engraved, says Jeremiah, with a chisel (an iron pen) on the tables of their heart. ie it is indelible. God wrote His law on stone, it was unchangeable.
This spiritual-medical condition has no cure. [Jer 17:9] to express it literally is illuminating; "it is Jacob and incurable". You will see the picture has changed slightly now. The heart was ruined by a law written on it; the law of sin and death? Now Jeremiah says it is twisted/Jacob. He is revealing, by means of two linked but separate ideas, that at the very centre of their being there was an incurable twist; its nature was engraved into it.
The particular sin, in Judah's case, was idolatry. The prophets used some pretty rich language, on occasion this 'twist' in Judah's nature is likened to donkeys in season. There is a relentless drawing in a certain direction and there is no known cure for this condition. It is the backsliding heifer; it is determined to go its own way.
We need to remember that this is the language that God has chosen to reveal truth. I don't really have a stone heart, nor a twisted heart, I have a blood-pump. Sometimes we need to sit loosely to Bible illustrations and just let them speak to our 'feelings'. I guess that everyone knew what Jeremiah meant and no-one could explain it. If you pressed them they would say, "yes, I know what you are saying".
The bible doesn't really teach that sin is located in one part of our being. It has percolated to every part, and infected every part. It is a fountain in our innermost being. The 'heart' cannot initiate a right move towards God, it will always initiate a move away from God. If it were the only influence touching our lives we would be absolutely without hope. But there is hope, but not from within. It must come from outside. Hence, Jeff's great verse in his post. There are many such comments in the Bible; He sent his word and healed them.[Ps 107:20]
Left to our own devices we can make no move towards God, but when He speaks we can respond. His current word has inherent power. Even a Lazarus can hear and respond.