***Total depravity means every area is tainted by depravity. In terms of "doing good things", unregenerate men would do "good" things by accident, as in every case he/she does so with some ungodly desire or end in mind, never with a desire to honor or bring glory to God on His terms.***
Let's say that a very wealthy man, who is not saved gives some money to save a Christian whose house is about to be repossessed and feeds him and basically buys him back from the mountain of debt he is under. There is a definite good done for the Christian. Does God not see this as a good thing?
Yet, I hear Calvinists tell me that the unregenerate man can not do anything good. They quote Romans 3:12 to me to prove this. But, it does seem pretty obvious that this unregenerate man has done something Good. Would this not mean that Romans 3 is meant only as a kind of Scriptural exaggeration. My brother Christian has told me the theological term for this.
I also think that I saw somewhere on this thread that the unregenerate man can do some good things and the example I used has the man doing this good thing on purpose, not on accident as you have indicated.
But, these good deeds are not acceptable to God, because they are not motivated by a love for God.
Hebrews 11:6, But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him.
If a Calvinist is taking Rom. 3:12 to say that the unregenerate cannot do objectively good actions, they're flat out wrong. That's not what Rom. 3:12's argument is; rather, its argument is that all are under sin (v. 9).
Rom. 2:14 earlier makes clear that the Gentiles, when they do by nature the things the law of morality demands upon them, are both defended and condemned because they sometimes do do what is right, and not all men have committed all sins. This is clearly pre-regenerate man.