Depravity robs the human being of any capacity for any impetus toward God, but does not incapacitate the human being from any response to God. A thoroughly depraved person can respond to the touch of God, the appearance of God, or the unseen spiritual influence of God without having to be re-plumbed or regenerated in order to do so. All that is required is for God to express himself sufficiently to that depraved person so as to stir that person's empty spirit.
Because of the autonomy of humans (an aspect of the image of God, marred though it is in them), whatever interaction the Spirit may bring to him or her is not guaranteed to overcome that human's depravity. If Adam and Eve could go their own way in Eden, then a depraved person under the influence of the Holy Spirit can do so as well (in fact, they're much more likely to). There is nothing irresistible about grace, anymore than there is anything not resistible about any instance of sin. That freedom of will is intended by God is readily evident in mankind being made in his image.
Ultimately, life as God would have it lived will require a complete rebuild. The combination of soul, spirit and body we have been born with since Adam and Eve is not capable of experiencing life as God would have it. Meanwhile, in the here and now, sufficient grace can be brought to bear upon our condition to at least enable reconciliation to and relationship with God. As any of us are naturally, we can be encountered by God and respond to him with faith; we can then even be regenerated and reborn in spirit despite our dying bodies; and therein do we overcome our natural depravity.
Ultimately, life as God would have it lived will require a complete rebuild. The combination of soul, spirit and body we have been born with since Adam and Eve is not capable of experiencing life as God would have it. Meanwhile, in the here and now, sufficient grace can be brought to bear upon our condition to at least enable reconciliation to and relationship with God. As any of us are naturally, we can be encountered by God and respond to him with faith; we can then even be regenerated and reborn in spirit despite our dying bodies; and therein do we overcome our natural depravity.