I think it is important to be clear about exactly what the "total depravity" doctrine states.
The doctrine of total depravity (also called "total inability") asserts that, as a consequence of the fall of humanity into sin, every person born into the world is enslaved to the service of sin. People are not by nature inclined to love God with their whole heart, mind, or strength, but rather all are inclined to serve their own interests over those of their neighbor and to reject the rule of God. Thus, all people by their own faculties are morally unable to choose to follow God and be saved because they are unwilling to do so out of the necessity of their own natures. (The term "total" in this context refers to sin affecting every part of a person, not that every person is as evil as possible.)
The statement that all people are unable to choose to follow God is a denial of man’s free will.
Does the Bible teach that man has no free will?
DT 30:19 This day I call heaven and earth as witnesses against you that I have set before you life and death, blessings and curses. Now choose life, so that you and your children may live
JOS 24:15 But if serving the LORD seems undesirable to you, then choose for yourselves this day whom you will serve, whether the gods your forefathers served beyond the River, or the gods of the Amorites, in whose land you are living. But as for me and my household, we will serve the LORD."
PR 8:10 Choose my instruction instead of silver, knowledge rather than choice gold,
ISA 56:4 For this is what the LORD says: "To the eunuchs who keep my Sabbaths, who choose what pleases me and hold fast to my covenant--
PS 34:11-14 Come, my children, listen to me; I will teach you the fear of the LORD. 12 Whoever of you loves life and desires to see many good days, keep your tongue from evil and your lips from speaking lies. Turn from evil and do good; seek peace and pursue it.
EZE 3:27 But when I speak to you, I will open your mouth and you shall say to them, `This is what the Sovereign LORD says.' Whoever will listen let him listen, and whoever will refuse let him refuse; for they are a rebellious house.
MK 16:15-16 He said to them, "Go into all the world and preach the good news to all creation. Whoever believes and is baptized will be saved, but whoever does not believe will be condemned.
JN 3:16-18 For God so loved the world that he gave his one and only Son, that whoever believes in him shall not perish but have eternal life. For God did not send his Son into the world to condemn the world, but to save the world through him. Whoever believes in him is not condemned, but whoever does not believe stands condemned already because he has not believed in the name of God's one and only Son.
JN 3:36 Whoever believes in the Son has eternal life, but whoever rejects the Son will not see life, for God's wrath remains on him.
JN 5:24 I tell you the truth, whoever hears my word and believes him who sent me has eternal life and will not be condemned; he has crossed over from death to life.
REV 3:20 Here I am! I stand at the door and knock. If anyone hears my voice and opens the door, I will come in and eat with him, and he with me.
REV 22:17 The Spirit and the bride say, "Come!" And let him who hears say, "Come!" Whoever is thirsty, let him come; and whoever wishes, let him take the free gift of the water of life.
The assumption that that man has the freedom to make a choice is the basis of all these (and more) verses. Man has free will. The notion that man is incapable of making such a choice is not compatible with the teaching of scripture.
God’s earnest encouragement to choose to serve Him permeates the scriptures. The notion that all mankind is incapable of doing so, that all mankind is “hard wired” to oppose God contradicts the teaching of Scripture.
ISA 1:18 "Come now, let us reason together," says the LORD. "Though your sins are like scarlet, they shall be as white as snow; though they are red as crimson, they shall be like wool."
ISA 1:19-20 If you are willing and obedient, you will eat the best from the land; but if you resist and rebel, you will be devoured by the sword." For the mouth of the LORD has spoken.
The phrase "if you are willing" requires that the person be able to exercise his free will.
This is one of many examples in scripture of how God deals with man; by giving man the freedom to make a choice. Total depravity resulting in having no free will is not Biblical.
iakov the fool
This was said to the Israelites. Obviously they did not or could not obey. And we know why. Jesus said they were not of God. But the question is not whether we have freewill or not. The question is whether our will is greater than God's will.
Jesus explained, 'No one can come to him unless the Father draws him.' John 6:44
Re. the flesh, total depravity is a bit strong. I agree with Paul. There seems to be a law at work in the mortal flesh to do what we don't want to do. I would explain it as a natural desire for money and pleasure.