This was my response:

All of you people should read "Ishmael" by Daniel Quinn  ^_^ 

God is sort of irrelevant when you look at the grand scheme of laws and the beauty of not being God.  

Anyway, in relation to the logical aspect of God existing, I must stab at this from the Buddhist perspective a bit.  When talking of existence at all, we must first consider what in fact does exist.  We need a control before delving into such a complex figure as a god.  We must look at the realm of the real with a critical eye and decide on one single reality if we are to as a group determine a logical progression which would lead to one thing either existing or not existing without the two happening simultaneously (by means of multiple realities).  Here we see our initial problem, the first of four, with logically deducing such a vast topic. 

We are forced to agree on reality based on flawed experiences and different perspectives by vote.  Now, if the vote is anything but unanimous, and I can be sure that I'll vote the one opposition if need be, then there is no fully agreed reality.  To say then that my vote doesn't count or it's a majority rule would mean that for a long time the world was indeed flat. 

This is a perfect segue into the next problem which is the problem of absolute truth.  We believe, or (better stated) must have faith in the idea, that our current science and logic are really showing us absolute truth.  The problem here is that we are basing our control on something which is in constant fluctuation.  This is clear in the rapidly changing aspects of quantum mechanics where we believe with great certainty that an electron will be within its orbital roughly 90% of the time but in reality it could be anywhere in the universe at any given moment.  This 90% is good, but hardly can suffice to be an absolute truth.  What we have from these tactics of reason is a discussion of the "general truth" and absolutely not an absolute truth.  Even a 99.99999999999999% accuracy is still not always right and thus while our laws exist in science as they are; they only stand against the test of time.  No matter how long something is considered right that is wrong, it's status as wrong does not change.  So while for now we must rely on this as a truth for perhaps even a thousand lifetimes, we can not wisely hold it as the only truth or an absolute truth for all time (which gods may or may not transcend). 

Reason three for the trouble with logical progression to God is that if it we use a purely logical argument, it would leave out all of the things which are not logical that can still occur in the realm of a deity.  To ignore the spontaneous and sudden discontinuity which a god or even a human is capable, can occasionally render a necessary leap for survival, understanding or even absolute truth.  Though this may seem wordy, an explanation Zen Buddhism uses is that when one achieves enlightenment or even a vast understanding of any kind (Satori) it rarely comes from a purely logical progression to that state.  For example, when learning to do a difficult physical action, let's say a hand stand, we can't simply be told how to do it and have it work immediately.  It actually takes repetition until your body finally understands the motion and balance required.  It is not a digital understanding but an analogue accumulation of knowledge which does not have a place in logic or science.  To say about A added to about B makes 35 is an entirely flawed statement.  Instead, we must make a leap to that 35 and apply what we can in our given situation and basically guess (an action based on logic but not necessarily the logical answer).  It is in this that we find the application of non-logic which yields results just as well, if not better, than logic in our assumed reality.

Finally, the most important aspect of this is that all of our experiences (the root of our logic) are based on fundamentally flawed concepts of the real.  O.K, look at your hands, then cross your eyes and see what happens.  You see perhaps three hands, perhaps two hands, perhaps even one hand.  However, this perception is subject to alteration and our reality is forced to change for that period of time.  This isn't to say that only sight is flawed.  The sum of a cold feeling and a warm feeling creates the sensation of a hot feeling to our touch, thus we cannot trust just the feeling of things.  We all hear things incorrectly at times, so where is the reliability of our ears?  Smell and taste are completely different to different people and so while many of us love chocolate and it smells sweet and pleasant to us, we can barely say that is the case for every person on earth.  In fact the dislike of chocolate is a genetic trait.  Are these people not perceiving reality?  Are they not trying to logically deduce one of the empirical things on which we supposedly agree?  "Chocolate is sweet, I like sweet things, thus I like chocolate," is a logical statement that can not be applied universally to all things.  Once we get to where it would have a logical accuracy, we have to deal again with the problem of testing every man, woman, child, animal, plant, vegetable, fruit, mineral, molecule, atom, and subatomic particle OR we can generalize yet again based on these analogue senses which are subject to change over time and are different for every individual and a virtually infinite number of possible realities. 

So we have four reasons not to use logic here.  That aside, as I re-read your question, I notice that you are asking for a logical reason to BELIEVE God exists.  So let's see what your sources for this can be...

What are valid means of knowing enough to lead to a belief?  If you want something as simple as experience, then I can give you no reason to believe in any god.  However, you can give yourself that reason by a series of experiences which validate enough for you to experience a god with your senses in one way or another (logically speaking though the senses may be flawed). 

Next you have the option of inferring God's existence.  You can say, "Well, so many things have serendipitously occurred in my life that I have reason to believe God exists." or even simply based on your experiences you can infer God exists just as you can infer that a deer has been through your yard based on foot prints in snow or mud, or that you found some fur, urine or feces which could belong to a deer in your yard. 

You could also believe the valid testimony of a trusted source.  If you trust your parents and they say God exists, why deny their idea (nb: I don't think anyone should indeed just trust their parents off the bat but they should in fact explore more ideas than the one into which they happen to be born.  However this is just my opinion which is clearly only worth the price you paid for it, nothing)?  If you trust the Hebrew Bible or the New Testament or the Koran or the Vedas or the Mahayana Sutras that tell about Bodhisattvas or the Tao Te Ching or traditional Greek and Roman stories or hieroglyphic details of gods from Egypt or any other texts which detail someone(s) or something greater than yourself, then go for it and believe in god(s) and/or goddess(es).  If you believe only science and logic's testimony, then you still lack a thorough quantitative explanation of the topic.  This isn't because the subject has yet to be tackled, but because we lack a method or a technology to accurately quantify God as 0 or 1 or >1. 

Conclusion:  While there is no one purely logical reason I can give you to personally choose to believe god exists, there are plenty of reasons that you have that allow you to make the non-logical progression to the existence of something greater than yourself.  It is our dualistic thinking that also says that God must either exist or not.  We have the option of saying that God Non-exists and that we must have faith in God as being beyond either of those simple ideas of our so called 'reality.'  So I suggest to you that you explore the possibility of this higher power existing all around you.  Just look at the ocean.  Can you still be the biggest, baddest, most knowing thing out there next to that vast body of water that is far bigger than we can actually conceive?  Sure you can, but to me, that sounds like a truly arrogant position to take.  We could better use our time helping the world (not OUR world) through faith, giving and seeking the truth, however difficult and non-logical it may be.

Thanks for reading!

          ~Raphael Falkoff

             B.A. in Religion and Asian Studies

             from Temple University

Please respond to this or message me your responses.  They can be either praise or critique but either way, be kind.  ^_^