The usual idea of "total depravity" has been distorted due to "total misunderstanding"!!! Please let me briefly explain what this shorthand-phrase actually means, because some Christian answers here demonstrate their lack of understanding of this Calvinist phrase:
It is about the correct assessment of the condition of the one who is to be saved. If we believe that the fall of man in Eden was merely partial, then we shall most likely be satisfied with a salvation that is partly attributable to God, and partly attributable to man. If a Doctor has a wrong view of a disease, his diagnosis and prescribed remedy will not deal with the disease! If someone who is diseased tries to make their own diagnosis and prescription but that very disease affects their thinking, they're not going to get it right!
Depravity can also be described as 'corruption', which is our natural state. We have been corrupted (by Adam) even before we were born. What this does NOT mean is the common misunderstanding, "Man is as evil as he could possibly be and unable to recognise the will of God and unable to do any good." What the Reformers at the Synod of Dort in 1619 meant was this:
When man fell in Eden, he fell in his 'totality'. The whole personality of man has been affected by the fall, and sin extends to the whole of the faculties - the will, the understanding, the affections and all else. See Romans 5:12, 2 Tim 2:25 onwards, Mark 4:11 onwards, 1 Cor 2:14, Psalm 51:5.
This, then, is man's natural state. Well, if we are 'dead' spiritually, can we raise ourselves to spiritual life? Can those in bondage free themselves? Can the blind give themselves sight, or the deaf hearing? Can the uninstructable teach themselves? Can the naturally sinful change themselves? See Job 14:4 & Jer. 13:23. No. We are like Lazarus in his tomb; we are bound hand and foot, corruption has already set in. But the Lord performs the miracle of grace. He quickens us, and makes alive those "who were dead in trespasses and sins" (Eph. 2:1). When the Lord performs a miracle, He does it perfectly. Nothing can go wrong when God's hand is at work. Nothing is left to chance, or with open-ended outcomes. All God's works are perfect and He brings about the new birth to those whom the Holy Spirit convicts of their sin. Therefore, even the 'total depravity' of man cannot stop God's miracle of grace! But, as Roman 2:14-16 shows, even the most rebellious sinner still knows God exists, therefore, as Paul shows, he is inexcusable. Nobody can plead 'total depravity' to excuse themselves! On the contrary - it only serves to utterly condemn us.
This point about total depravity in Calvinism is not the same as the point about predestination. They are two distinct subjects, or points. But if the correct view of total depravity is understood, then it can be seen that God's predestining prerogative would be utterly necessary to overcome the totality of man's sinful condition.
The Five Points of Calvinism (booklet) by W J Seaton (Banner of Truth Trust)