When Adam forsook God and was justifiably cursed by him, his innate connection to God was broken and his physical being was stricken with death. Adam was cast from the presence of God (the place where God walked) and frustrated in his relationship to the biosphere and with others of his kind (Eve to start). The individual became an island unto himself (so necessarily sinful) with no ability to get back to God, nor to truly understand and relate to him nor, for that matter, to do so with his fellow human (as seen from Jesus' high-priestly prayer). Locked in a self-absorbed prison of death and decay separated from God, debauchery ensued. If God did not initiate contact with humans, no contact, no interest, no desire would be forthcoming from Adam's kind.
Hopefully, it is evident that humankind's depravity should not be seen as something that renders humankind incapable, even in their depraved state, of responding to the interjection of God. God showing up in a way that can be responded to is sufficient in itself to break any barrier that would have kept fallen, natural man in the dark concerning God. Such is demonstrated over and over again throughout biblical history (e.g. Noah, Abram, Moses, etc.). To posit a theory in which God has to fix the depraved human being (i.e. regeneration) before that one can respond to him is unnecessary and not validated by scripture.
The truth is that what makes humans depraved in the first place is a lack of God in their lives. People are depraved in that they are like God (i.e. in his image) but are apart from and without God who's presence is what makes that image work properly. In their depravity, they have no desire to have God (as he truly is) in their lives. What they need they neither discern nor want. When God comes near in the mysterious ways that the Holy Spirit can, that lack is addressed at least to the level that the fallen human is able to see, hear, and respond to what wasn't there before. None of this requires any change in their nature and none is ever mentioned throughout the biblical record.
Human beings always had and have always maintained since the Fall the spiritual capacity to recognize God. That capacity was not such that it could independently discover God or engage him on the basis of executing that capacity in and of itself. God's direct intervention is necessary for each and every human being to come to know and understand him and his ways, but upon that divine intervention, awareness of what we otherwise would not have been aware becomes possible. However, if Adam in all of his pristine purity and perfection could ignore and forsake divine connectedness, than so can all his depraved sons and daughters.
Even the best amongst humankind is totally depraved, broken beyond their ability to help themselves--and yet even the most depraved among us can respond to the gracious visitation of the Holy Spirit. Depravity will continue to be an issue for us until Christ returns and our old dead, depraved natures are done away with once and for all, and new nature completely like unto Christ's is put in their place. That, of course, is predicated upon turning to Christ now. So let me ask you, have you responded to the Holy Spirit drawing you to Christ yet?