1. Logic and math
Only monotheism makes sense of what logic and math is. Pleading evolutionary origins of logic reduces the use of logic to nonsensical. If logic and math are merely the result of naturalistic processes, then how can they be trusted to lead us to truth at all? Even truth itself becomes absurd. As Pilate said famously 'What is truth?'
However I see that math is objective, it comes from outside of ourselves, and that is internally consistent. Gödel saw the same thing and noted that because numbers are uncountable (infinite) and well-ordered there must be an intelligence behind them that is not human.
Logic is intrinsically true, not because it works in practice (saying that is circular reasoning—logic works because it works) yet because it must have come from the author of truth outside of time and space. Merely assuming universal, invariant, immaterial laws is no explanation and they demand an explanation.
Instead of the God of the Gaps, God is inferred as the properties of God match these universal laws. Infinite, eternal, height of intelligence, constant, non-contradictory.
Logic and math contain His fingerprints all over them.
2. Morality as a system
The major arguments against God are often moral, yet I find morality existing in itself as a great argument for God. There must be some higher standard for humans to attain to—a Moral Law. A Moral Law transcends humanity, this universal law requires a universal lawgiver.
If right and wrong are what we decide for ourselves as humans, then morality is reduced to mere whims and wishful thinking. Justice and injustice cannot exist in such a system, as what is unjust to one person (like robbing you) might not be unjust to someone else (as the robber I might legitimately feel I deserve your money). So who really is right without a higher moral standard than our own opinions?
When people say that God is immoral, what are they judging Him by? What standard? God cannot be immoral though if you factor in eternity. If there is an eternity wrongs will be righted and have a purpose. Proving the injustices in this world matter immensely to God. God being just can be seen not by what we observe in this world, but what happens in eternity.
The moral system in Christianity is undoubtedly the highest system of all. Being unique as it makes us accountable for our thoughts and intentions as well as what we do.
3. The inadequacy of other worldviews
Logic matters. Now that I've got that axiom to rest on, I can evaluate all other world systems as being logically consistent or inconsistent. Given that every touted inconsistency about the Bible has been answered by scholars as being due to cultural and linguistic misunderstandings, I can see that Christianity is logically coherent. But what about the other worldviews?
James Sire's The Universe Next Door has long been the text for examining worldviews up against the Christian system. This book has shown the other views to be woefully inadequate. While it doesn't assess the cults, there are numerous other materials out there defeating cultic writings.
Naturalism must necessarily lead to nihilism unless you become an existentialist or postmodernist and both those views take an illogical 'upper story leap' to use the words of Francis Schaeffer. No one can live consistently upbeat when noticing the lack of purpose and certain death they face. New Age is eclectic, it borrows from a vast range of ideas, which means that you can get no unified, coherent system.
Reason cannot be separated from God
Those three points are pretty solid reasons to believe. The coup de grace to Christianity has not been issued, and I can't see that it ever will be based on the points above. If you must use logic to defeat God, you must make an ontological account for logic. If you can't account for it your worldview falls apart.
If you have a worldview that says logic does not exist, then absolutely everything human falls apart—math, science, health, technology and all other human endeavors. The Christian God of love, justice and rationality allows us to keep our reason.
I prefer to be reasonable, hence I believe in God.