"Totally" could mean what you say, but that obviously isn't the way it is used by those who believe in it. It describes a current condition which IS changed by the power of God. The point of it is that we cannot come to God on our own. Our separation is total. No matter how smart we are, and no matter how strongly we perceive our inner goodness, we are going to be lost without divine intervention. It is "dead" vs. "wounded". God raises the dead.
More correctly, the definition should be "partially depraved", since our motives are very rarely totally evil.
I think that would be the Catholic position, since you believe we are born with inner goodness that we use to cooperate with God. Total Depravity is meant to distinguish from that.
We agree on that, but I believe "total depravity" means we do nothing WITH God. God does everything in this construct. Our choice is nowhere in the mix, which makes God the sole decider of whom will be saved, although God "desires ALL men to be saved". As a result, I cannot agree that God does not take into consideration our own choice, even though it is imperfect and cannot come to God by itself.
I believe we do possess the desire, latently, to unite with God. We all desire happiness and we all enjoy beauty and truth and goodness, at least imperfectly. Our position is wounded, which still maintains that we cannot come to God alone.
Regards