The original post misses the meaning of T [total depravity] which simply means that all man's faculties were effected by the fall [defaced, not eliminated].
I think it was Reinhold Niebuhr who said that this was the only doctrine for which we had empirical evidence!
I have heard Calvinists say that the 'L' is a bad choice of terms but then, they could not spell Tulip if they changed it, cf. http://sdcougar.startlogic.com/blog/?p=179
Whatever the Calvinist specific definition is, when you say something is "total" that defines the something as "without exception". Thus, if man is "totally depraved" then there is not one thing a man could do that was not considered depraved (Synonyms include; corrupt, perverted, debased, immoral, degenerate, etc ). We know from the scriptures and from observation that a man (speaking in general terms, unregenerate) can do non-depraved things.
What you here mainly from the Calvinist on this subject of Total Depravity is that man has no ability to choose to call upon Jesus Christ for regeneration/salvation because they are Totally Depraved. They believe this and defend this even though the scriptures show God pleading with sinners to believe and repent.
I was listening to Ravi Zacharias this week in an Q&A on this topic of Sovereignty verses Freewill. He sees this the way I have come to see this from the scriptures and that is that both are true and held in tension one against the other throughout the scriptures. Freewill does not destroy the sovereignty of God, but rather is part of God's sovereign design.
Election is as Peter said, "according to the foreknowledge of God". Within the foreknowledge of God lies the foreseeing of those whom freely choose to believe after having been drawn by the Father, convicted by Holy Spirit as sinners, called to believe on Jesus Christ. Many are called, few are chosen. The chosen are they which choose to call upon Jesus Christ.
Their are extremist on these points. The Calvinist wholly embraces Sovereign Election at the expense of Freewill choice. The Armenian wholly embraces Freewill at the expense of Sovereign Election. When hermeneutics is appropriately applied we find no contradiction at all. Balance must be applied, both are taught in the scripture, thus, both must be true. It is up to the student study and rightly divide the word of truth to strike that harmony between the two truths.
If I focus solely upon those passages which speak of Election and God's Sovereign will, I will no doubt have to conclude the Calvinist pov correct. If I focus solely upon those passages which speak of Freewill choice, I will no doubt have to conclude the Armenian pov correct. But if I stay focused on all passages which speak of both the Sovereignty of God's will and the Freewill of the person, then I can clearly see the truthfulness of both and find that pov which allows the whole of God's Word to go forth.
In God's Sovereign Will, God has designed the Freewill Choice of man to believe on Him or reject Him. That is what I have concluded upon considering this controversy over the past years of study.