Meaning of Total Depravity
Total depravity doesn't teach that we are all as bad as we possibly could be in a practical sense. Total depravity simply means that every part of our being is corrupted by sin. And specifically, that our will, our human will, is bent in on itself, so that we will not seek God, we will not choose God, in and of ourselves. We need God's effectual grace, His powerful working, to change our hearts, and to change our minds, so that we do choose Him.
So total depravity is really about our inability to do what God calls us to do, because of our own sinful corruption. And an understanding of that helps us to appreciate the wonderful grace and mercy of God, who seeks those who are not just lost, but who are wayward and stiff-necked and rebellious. And He gives us a heart.
The scripture says that this new covenant promise is that God will take away our stony heart and give us a fleshy heart, a heart that beats with love for Him. That's the difference between being totally depraved and unable to come to God on our own, and His grace that invades our lives and makes us new creatures.