One thing I found helpful in this chapter of Groothuis' Christian Apologetics was the distinction between general revelation and natural theology. Not all general revelation is 'natural'--"God may have revealed himself in a way not susceptible to argumentation. If so, this general revelation would be more a matter of intuition than intellection," (p. 174). I think the moral hunger common to every human fits in this category.
I appreciated that general revelation in the Bible was referenced. Romans 1:19-20: "What may be known about God is plain to them, because God has made it plain to them. For since the creation of the world, God's invisible qualities--his eternal power and divine nature--have been clearly seen, being understood from what has been are, so that people are without excuse." Romans 2:14-15: "(Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)"
The "biblical authority" argument against natural theology fails because an authoritative text is not made less authoritative (is not undermined) by corroborating and confirming its authority (defending its credentials)--rather, these things establish the authority of a text, which is not dependent on such arguments, but is made more credible to (say) skeptics.
The "noetic effects of sin" argument against natural theology fails because "Reason itself cannot be fallen and remain reason," and "Sound reasoning is the norm for [those] willing to follow truth wherever it leads."
The "direct knowledge of God" argument against natural theology fails because there is more than one way to know something--theistic arguments can supplement immediate knowledge.
The "proofs lead to pride" argument against natural theology fails because theistic arguments can influence a person to begin to wonder about his or her status before God, to seem small in comparison to the metaphysical grandeur of God, and to investigate the claims and credentials of Christian theism.
The "natural theology in competition with special revelation" argument fails because "the Bible itself claims that God is revealed in nature and conscience" and "a sound apologetic method attempts to verify the Christian worldview through various means, not merely by natural theology."
The "religious irrelevance" argument against natural theology fails because, rather than ending in deism, it is a "prelude to other evidences and arguments pertaining to" the creeds of Christianity.
The "complexity of proofs" argument fails because many reason these arguments on their own without ever first learning the arguments, and many master them--so it must not be too complex for them. The argument does not apply across the board and so does not eliminate natural theology altogether.
The "rational weakness" argument fails because it poisons the well rather than giving actual counter-arguments. "In the end, the proof of the theistic proofs lies in the proving, that is, in their validity and soundness, and not in theoretical musings about what they can or cannot or should and should not do. We must simply discover whether the arguments, singly and taken together, make belief in God more credible than otherwise."