The doctrine simply means those affected by sin cannot and do not approach God in their own might for salvation. TD is the effect of sin than the nature or ability of the sinner. TD does not have anything to say about whether or not a sinner can do moral good in other areas of life. It makes no claim the person who has sinned is only totally morally and spiritually depraved. These are common misconceptions about TD and many a strawman has been argued because of these misconceptions. The doctrine is limited specifically to the matter of salvation.
That is not to say sinners aren't affected by sin in other ways. Sinful humans are capable of morally good acts and morally bad acts, but even a morally good act done in the sinful flesh has no salvific merit. God might commend it as a good act but works do not save, especially not works done by sinful flesh. Simply put, sin does not affect salvation from sin.
It does not help that there is enormous inconsistency from teacher to teacher. Reformed teacher Steve Lawson over at R. C. Sproul's Ligonier, for example, states,
"The doctrine of total depravity does not mean that all humankind is as evil as it possibly could be. Rather, it means that sin affects the whole person. We are born corrupted, poisoned, and polluted by sin. Our minds are darkened and we cannot see or understand the truth. Our hearts are defiled so that they do not love the truth. We love what we should hate, and we hate what we should love. Our wills are in bondage to sin, and we cannot believe the gospel in and of themselves. We sin because we are sinners and because we have a sin nature."
R. C. Sproul himself wrote,
"In the Reformed tradition, total depravity does not mean utter depravity. We often use the term total as a synonym for utter or for completely, so the notion of total depravity conjures up the idea that every human being is as bad as that person could possibly be.......... So the idea of total in total depravity doesn’t mean that all human beings are as wicked as they can possibly be. It means that the fall was so serious that it affects the whole person. The fallenness that captures and grips our human nature affects our bodies; that’s why we become ill and die. It affects our minds and our thinking; we still have the capacity to think, but the Bible says the mind has become darkened and weakened. The will of man is no longer in its pristine state of moral power. The will, according to the New Testament, is now in bondage. We are enslaved to the evil impulses and desires of our hearts. The body, the mind, the will, the spirit—indeed, the whole person—have been infected by the power of sin."
We're not as bad as we could be. We are not
utterly depraved, only
totally depraved




. To be as wicked as we could be would mean no moral good could occur. Seth could not worship God, Noah couldn't build a boat, Abram couldn't leave Ur, etc. Remember TULIP is specifically about salvation. The "T" in TULIP is therefore, specifically about salvation. Because the effects of sin are total, we cannot act to affect our own salvation.