Man is Totally Depraved in that, in his unregenerated state he has no desire to draw near to God. It is not that every action is evil, but no action will be pleasing to God. Unregenerated man cannot and will not choose to follow God. God has to regenerate man first. Therefore, all who come to God do so at God’s will, not man’s.
Romans 3:11-12
None is righteous, no, not one;
no one understands;
no one seeks for God
All have turned aside; together they have become worthless;
no one does good,
not even one."
I'm not sure when you consider a man "regenerated", I have to guess you talking about being born again as a new creature? If so this is certainly something that happens upon condition of faith. Moreover always happens given those conditions according to John 3:16.
But then, deciding to have faith in God seems like a decision of the individual to me. Indeed, the central most important decision of our entire existence.
It seems odd that such a decision could be made without any desire at all to draw near to God.
Thus, for consistency, I can see why the Calvinists must reject the concept of free will in the matter. I will grant that these doctrines give mutual support, but I can't see much motivation for either outside of a perceived contradiction between God knowing what man will decide ahead of time, and yet still allowing man to choose.
Reading C.S. Lewis has cured me of supposing there is such a contradiction.