From a scientific stand point it is not illogical to believe God doesn't exist. 

Do you believe its illogical to think pink unicorns or flying pigs don't exist?

 Are you implying that absurdity is a proof against existence?  Because, if you are, then you would have a reason to disbelieve it, as then the evidence would tip in favor of nonexistence.  But if absurdity is not (which it isn't), in and of itself, proof against, then there is no reason to assume something doesn't exist.  And, when you get right down to it, saying this computer I'm typing on exists is no less absurd than saying the flying spaghetti monster does.

You may actually be the one with your head out of the clouds on this one.  It seems to me that your addition looks at the difference between the literal possibilities that we know of versus the theoretical possibilities.  Showing that while we can swirl ideas around in our heads which make perfect sense in the path we have chosen for our deduction, they may not necessarily reflect what is plausible in practice.  However, I still believe that in God being all powerful in that He made all of the rules of this existence, that He would even transcend what we commonly accept as practical based on the reference point that we have to work with, our existence and our established thought patterns.  If we were to expand logic closer to it's outer reaches, then I think it is actually possible for God to, in your phrasing, "do something He cannot do."  But perhaps not within the literal bounds of this existence.

Lots of good stuff.  Here, as well, there is again an implication that logic is a relative term to the circumstance with which we confine it and in turn is limited to our current knowledge and since we are subject to psychology, we can also say our current "accepted" knowledge.  If logic wasn't a relative term here, then you would have to coin that it is "scientific" that pink unicorns don't exist, but then you are saying that science isn't logical, in which case it would potentially be an inferior process as it would not be considering all possibilities, which could house a correct possibility not considered.  Just thought I would bring that tidbit out for my past posts, but all your points are well made.

While I must (respectfully) disagree, in that I find logic to be unchanging at any level, and that God is "bound" by logic (although that isn't the apt description), we can both agree that the rock question isn't a problem, eh? :)

Ah well there in lies a question of how we define God.  The initial assumption that God is all powerful would seem to imply that He transcends all we know.  Which brings us to how we define all powerful.  If you simply define all powerful as what can be within the confines of our known existence, then you are not considering the possibility that He created all that we know to exist.  In which case, He would thus transcend all that we know.  If you are saying that God is "bound" by logic then He cannot be all powerful in the fullest extent of the concept. 

My argument and explored idea is that He has actually made logic as we know it, and that undiscovered qualities of our existence may actually be far beyond our current levels of thinking and logic.  So much so that our currently accepted logic does not apply.  Which brings me to my prior posts about logic being a relative term and since possible scenarios for which to create and apply logic are also limitless technically logic, in this case, would be boundless, and thus if God is "bound" by logic, then in this case, He would be boundless and again the fullest extent of the concept "All Powerful."  I believe it is also possible that God IS theoretical embodiment of the truest form of logic which also fits into some beliefs that God is omnipresent and would also imply that He has been forever changing, but in that He has always been and is forever changing for all possible changes, then He has actually been forever the same.

Why are there so many shitty people?

I hesitated to use bound, for I do not think that correct.  And I can agree with you that God might embody logic.  But it is with that that I find God "unable" to do absurd or meaningless things, in that a meaningless "thing" cannot be done because it does not exist.  To say God cannot do what isn't is limiting; it's definitive, as the alternative says nothing (and thus is not limiting).  Also, I think it false to say that there is "our logic" and then there is "God's logic".  There is no such distinction, for logic is simply non-contradiction.  One might say that we don't always use logic correctly or get it wrong occasionally, but that does not imply there is a different logic to be had.  Furthermore, the argument "God does not have our logic.  This action a contradiction.  Therefore, God can do this action" is using "our" logic again to prove our logic isn't the highest form of logic, and thus defeats itself (which is logical).

All science is based upon the world in the scenario as we know it to be and through the limited senses that we have to percieve with.  We created all the core structures that we use to determine whether something is scientifically sound or not.  And while they may coexist with our observations in enough cases that we do not completely discredit them, the possibility that there are more accurate methods which reference the world in its entirety as opposed to simply how we percieve it is always present.  They get us by, but they may not be perfect.  To state that they are perfect would be to imply that you know as truth that there is no other possibilities, which cannot be as we may not have observed what is necessary to know that.  So while we break new ground and discover new useful information and processes, we are doing so at the risk of being wrong.

Science in many ways is about function, not truth.  Like walking.  It may not be the best form of travel if we were to know every invention that could ever be created and every principle that could ever be discovered, but it works, we know that, and so we use it.

Actually I've been saying that "logic" or truth is possibly relative to the environment in which it is applied, and if it is relative, then there are an infinite many number of subsets to which can be in the overall set of logic.  I am saying that while our logic may be a subset of the overall set of logic, with God possibly being the whole set of logic, our subset would not equate the set since there are many logical environments that exist that we do not know about.

Oh and guys, I really appreciate you allowing me to explore thoughts like this.  I'm enjoying these discussions.  Not sure when my mind is going to give out though.  lol.  The mind has been shown to take up the most energy of any other body part.