Theological determinism is the thought that everything occurs because God determined it would before it did. When he actualized the creation, everything followed, and follows, the course decreed for it by God. It is a logical consequence of God's sovereignty, if freewill is not factored in. There are some subtleties and some variations that are possible, but in general, that is how I take determinism.
Total Depravity, in Calvinist theology, is the doctrine that mankind was so flawed by Adam's sin as to be rendered utterly incapable of any true good, without any ability or desire whatsoever to perceive or believe God or to walk according to his command. The doctrine is actually very similar in Armininian conceptions, except, most strikingly, that Arminians believe faith can arise in the depraved through the assistance of the Holy Spirit, whereas Calvinists believe faith cannot occur until the depraved has become the regenerated (i.e. born again).
The question that has been roiling through my brain is how the two theories can be held without excluding one another. If determinism is true, then mankind is not depraved, but is exactly, no more and no less, what God willed and wants them to be. If they are not, only he could be at fault, for only his will carries any weight!
If freewill is an illusion, then so is depravity, at least in any moralistic sense. We are merely as we are programmed to be, and do exactly what God determined for us to do. We are not incapable of walking in God's will, but in fact, whatever we do is precisely God's very will. That doesn't sound depraved to me.
I don't think anyone would posit that a furry little shrew is depraved, because it is and does what it is meant to by God's determination. If we are and do what God has determined for us, then I say, neither are we depraved. But since the scriptures are more than clear on the subject, I say determinism will have to go by the wayside.