While I would agree that the doctrines of grace are axiomatic to biblical interpretation, I am curious as to the best articulation of Total Depravity. Total Depravity expresses the reality that all areas of life are tainted by sin. Since the Fall of Adam, natural man is entirely influenced by sin. This depravity is expressed in different degrees for different individuals. Thus the murderer and the mystic are both totally depraved, yet their depravity may exist in varying degrees of depth.
The question is, Does total depravity posit that no unbeliever will demonstrate a 'seeking' of God? (though never to find him outside of Christ). Does it argue that the works, thoughts, and art of the natural man are worthless in aiding us to know God? For example, can a pagan paint a picture that is 'God-reflecting'? Can an agnostic express philosophical truth clearly enough that it actually helps Christians to better understand God? Can a musician who knows nothing of Christ's atonement produce music that is valuable to the pursuit of knowing God?
Now, of course the typical cautions need to be explicit. The pervasiveness of sin is not the issue. Naturally man is sinful, rebellious, and treacherous towards God. To study any area of human existence without God is to study the ruin of the image of God, and I certainly wouldn't advise a Christian to delve deep into the teachings of Buddha or Bertrand Russell to know God more. That is not the issue. The issue is does this ruin mean 'worthlessness' or 'unworthiness'?
The apostle Paul can quote the OT "There is no one...who seeks God" (Ro 3)and he can say to the pagan Athenians "Now what you worship as something unknown I am going to proclaim to you." (Acts 17) Explain the paradox...