It is total; however, as a part of becoming saved/born again, God discards the old natural man within us in its entirety and replaces with the new man. God does it all, man does nothing.
You are still not thinking clearly, and do not understand what the verses you quote are saying.
OK...
Here!
If God, as you say, discards the 'old man?'
What is God left to work with?
If man is TOTALLY depraved?
TOTALLY...
To discard the old man?
Would mean a man would vaporize and no longer exist.
You keep forgetting that our depravity came from Adam's procreation.
It's the body that is the culprit.
The soul is enslaved to the body.
Eliminate the body and have the soul be alone?
That soul would have the ability to make a choice for God if the Holy Spirit was enabling that soul to see what is required to make a choice.
Grace isolates the depravity of the flesh over the soul, so that soul would be as good as outside the body in the effect.
Grace found a way!
The only thing God forces to happen while a person is being witnessed to by the Spirit, is to have the flesh shut up,
and leave the soul be, to make up its own mind.
That is why God saves the soul, not the body.
I have been crucified with Christ! Galatians 2:20a.
grace and peace .........
........