As we think about the Calvinistic doctrine of 'Total Depravity', we should remember historical context of the TULIP. Total Depravity is a doctrine that was used to counter a false doctrine of human sinfulness.
Arminius' students had put forth a doctrine that stated
"Man is so depraved that divine grace is necessary unto faith or any good(Taken from: Roger Nicole, "Arminianism," Baker's Dictionary of Theology, p.64.)
What's wrong with that doctrine? On the face nothing. But put together with the rest of the 'Arminian' doctrines and read in that context we find a new meaning. The 'Arminians' believed that God gave everyone this 'Divine Grace' and then left the will to do what it willed. Or that God gives everyone the opportunity and ability to believe and then leaves the coosing up to the sinner. They believed that the will of man could choose good or evil. They believed that the will was left untouched by the fall. The 'Calvinists' responded, "No, man's will is so affected by the fall that man will not choose God." This is the meaning of 'Total Depravity'. It is the biblical doctrine of human sinfulness. We have been so affected by the fall that sin is present in every part of our being. Sin is present in our minds, hearts, souls, spirits, and strength. We are corrupt. This is what 'Total' means. The whole man has been corrupted by sin.
A common misconception about this doctrine is that man is as bad and as bad off as he can be. This is not true. God has not allowed anyone to reach the depth of depravity that they are capable of. He has restrained us. Obviously, He does allow some people to go deeper into their sin than He does others. And yet, all have sinned, and all are destined for an eternity in hell because of their sin.
'Calvinists' also teach that man is capable of doing some good things. Some people give to charity, love their spouses, feed the poor, are honest in their business transactions, etc. But the flip side to this is found in Isaiah 64:6-8. All our goodness is inthe eyes of God 'filthy rags'. Our good deeds are like bandages that cover a wound but do not heal. They are bandages that cover our corrupt, rotten, dead flesh but do not produce new life. As many good things as men are capable of doing we must remember that mankind in general does not follow God. They run from God. It takes a work of grace by the Holy Spirit to overcome the will of man that has been overcome by sin.
'Total Depravity' means; not that man is incapable of good, but that sin permeates every aspect of our being, the will included. Man never seeks God or His glory, but seeks his own good and is, in essence, his own 'god'. Since man has a sinful nature, he sins, and must pay for his sins. All mankind is destined for hell from the outset, because of the presence of sin in their lives.