Jean Calvin, answered from the texts and cited to the page.
The question is one I have addressed not once but across many years of exposition, and the answer requires care on two fronts: what the doctrine asserts, and what it does not. When Adam fell, he did not merely sustain a wound that left the greater part of his nature intact. He lost original righteousness entire, and with it he propagated to all his posterity both that privation and the vicious habit of concupiscence that wars perpetually against the higher powers of the soul.1
Every man born into the world carries this from the first moment; none is exempt.2 The Papists, pressed by the ancient testimony, will concede that Adam lost supernatural gifts and that natural ones were corrupted — but then they hold back, feigning that some part of reason remains sound and that the will was wounded rather than destroyed.3 The Prophet's word refutes them: God does not promise a repaired heart but a new heart, a new spirit; and if the whole must be made new, then the soul is not merely injured in each part but so corrupt that its depravity may be called death and destruction, as far as rectitude is concerned.4
Total depravity, then, does not mean that man has ceased to be man, or that the faculty of will has been annihilated. The will remains — it is hereditary, part of the creation, and Adam's fall could not blot it from our nature.5 What perished is the soundness of the will. Bernard put it well enough that I have cited him: simply to will belongs to man; to will what is good belongs to grace; to will what is evil is the corruption of nature.6
The will rushes into sin with the strongest propensity, not because it is compelled from without as a stone is moved, but because it is bound from within — and a necessity of this kind no more destroys voluntariness than God's necessity of being good destroys the freedom of his will.7 The doctrine is total in this sense: the corruption extends to every part.
Reason, affection, will — none retains a sound and entire motion toward God.8 The virtues that men produce by their own motion, what I call the moral virtues of the heathen, flow from a will that is weak and injured; they may be applauded in civil courts and in common estimation, but before the celestial tribunal they possess no value to merit the reward of righteousness.9
Conversion to God — the very first inclination toward him — is attributed in Scripture solely to divine grace, not to any residual capacity the sinner has preserved through the fall.10 That is the doctrine. It is not a counsel of despair; it is the ground on which grace becomes grace rather than assistance rendered to a creature already partly on its way.
after our first parent did contrary to what God had commanded, he incurred the penalty appointed by God, and lost the most fair gift of original righteousness. Hence there was a want of this righteousness, together with a vicious habit of concupiscence, which is perpetually at war with the spirit and the higher powers of the soul.Tracts Relating to the Reformation Vol 3
This sin, together with concupiscence, he propagated to all his posterity, so that all men whatsoever that come into this world are born with it, and none is free from it, not even the child of one day.Tracts Relating to the Reformation Vol 3
The Papists do not deny that free will is injured and wounded, but as I have already said, they hold back something, as if men were partly right by their own proper motion, and some inclination or flexible motion of the will remained as well towards good as evil.Commentaries on the Prophet Ezekiel Vol 1
if there is need of a new spirit and a new heart, it follows that the soul of man is not only injured in each part, but so corrupt that its depravity may be called death and destruction, as far as rectitude is concerned.Commentaries on the Prophet Ezekiel Vol 1
the will is naturally implanted in man, whence this faculty belongs equally to the elect and the reprobate. All therefore will, but through Adam's fall it happens that our will is depraved and rebellious against God: will, I say, remains in us, but it is enslaved and bound by sin.Commentaries on the Prophet Ezekiel Vol 1
Bernard properly observes, that we all have a power to will; but that to will what is good, is an advantage; to will what is evil, a defect. Therefore simply to will belongs to man; to will what is evil, to corrupt nature; to will what is good, to grace.Institutes of the Christian Religion Vol 1
if a necessity of doing well impairs not the liberty of the Divine will in doing well; if the devil, who cannot but do evil, nevertheless sins voluntarily; who then will assert that man sins less voluntarily, because he is under a necessity of sinning?Institutes of the Christian Religion Vol 1
God pronounces that he gives to his elect one heart and a new spirit. It follows, therefore, that the whole soul is vitiated, from reason even to the affections.Commentaries on the Prophet Ezekiel Vol 1
The virtues which deceive us by their vain and specious appearance, will be applauded in civil courts, and in the common estimation of mankind; but before the celestial tribunal they will possess no value to merit the reward of righteousness.Institutes of the Christian Religion Vol 1
The will, therefore, is so bound by the slavery of sin, that it cannot excite itself, much less devote itself to any thing good; for such a disposition is the beginning of a conversion to God, which in the Scriptures is attributed solely to Divine grace.Institutes of the Christian Religion Vol 1