I appreciate the way you are asking and will try to do your question justice.
Well, I don't actually "believe in God", since I'm an avowed agnostic. But like the later Anthony Flew (at one time the atheists' atheist), I do find myself drifting towards something like deism I guess. That probably requires some explanation.
Like George-ananda wrote earlier, one needs to ask what concept of 'God' we are talking about. They aren't all the same. I personally differentiate between the highly personalized deities of religious myth, and the far more abstract object of natural theology.
When it comes to figures like Yahweh, Allah or Vishnu, I think of them as fictional characters in effect. I believe (but not with 100% certainty) that they don't exist in any literal sense. So that puts me close to the atheists in that regard. I don't believe that the Bible, Quran or the Gita provide me with any privileged insight into the ultimate nature of reality. I basically reject most revelation claims.
But I don't totally dismiss these traditions either, since a lot of very good philosophy of religion has been done in the Christian, Islamic and Hindu traditions. I feel lots of kinship with the neo-Platonic strands of Christian tradition for example, and perhaps for Palamite theology in the Orthodox tradition. I am not ready to totally dismiss religious experience.
That being said, as an old philosophy major, I feel myself surrounded by mysteries at every moment. It's the human condition. We can ask "why" about anything. We get an answer. So we ask 'why' about the answer. And without exception we find ourselves at the frontiers of human knowledge in just a few iterations. Try it with your words up above: 'reason', 'logic', 'evidence' and 'facts'. What do those words mean exactly? What grounds and justifies them? Those are all still open philosophical questions and there's a huge literature about each idea.
So human beings find ourselves surrounded by unanswered metaphysical and epistemological questions wherever we turn. Something is going on with all this "reality" stuff, and I don't think that any of us really knows what it is.
One of the traditional ways of conceiving of 'God' is to think of the word as referring to whatever the ultimate answers are. We see it with the ancient Greek philosophers like Aristotle. This "God of the Philosophers" would be whatever the ultimate irreducible ground of reality is and whatever the source of the order is that we (and science) preceives around us, and ultimately why there is something rather than nothing. The ultimate answers to the ultimate questions.
I just feel intuitively that there's more to all this than we know and I long to know what it is. (Though I've long been resigned that I never will.) That's what I see religion pointing towards and it's why I don't want to sneer that search, that openness to the unknown, into atheist oblivion.
As an agnostic, I can't be sure that answers even exist. But just emotionally and psychologically, I'm inclined to take the Principle of Sufficient Reason seriously -- For all x, if x exists, then a sufficient reason for x's existence exists. (Yes, I'm aware that it leads to infinite regresses.) Science generally accepts it without acknowledging it, it's what the principle of causality is all about. It's why when we ask how birds fly, we aren't satisfied with 'It's just the nature of birds to fly and that's that'. We want to understand how it's done. It's what separates us from our dogs, we don't just accept our surroundings as givens.
I certainly can't be sure that the answers to the most fundamental questions can ever be known by beings in this reality. If there are super advanced space aliens out there, they probably don't know either. That's my suspicion.
I don't know whether it all traces back to one Master Answer as the ancient neo-Platonists thought: The ineffable transcendant "One". The Utimate Mystery out of which everything else emerges. Or whether there are multiple independent answers to different questions. Or even whether human concepts would apply any longer. I certainly don't want to think of the answers as human style "persons", that seems to me like the height of anthropocentrism.
I guess that I think of the God of the Bible, Quran and the theistic Indian traditions as very human attempts to put a human face on the ultimate transcendant Mystery that I feel so strongly, so as to make it more comprehensible and emotionally comfortable.
Human beings find it much easier to relate to people than to understand abstractions. Just think of high-school kids hanging out with their friends, vs trying to learn algebra. The former is a far more complex data processing task than the latter. But it's human.
So I often feel some kinship with religious people I guess. I sense that they are on a similar quest.
your comfort in science and its answers that give you a fullfilment in life