The following are what my biblical studies have led me to conclude. I cannot vouch for the validity of any of them, for I am only human and am prone to errors, sometimes more than others.
First off, I'm sure you understand the reason for the Bible being divided into the OT and the NT; the whole dispensation thing. Life under the Law and life under Grace and all that. I view the OT as a history book of sorts. It also shows us, especially those of us that aren't Jewish, what Christ has saved us from. No longer are we subject to the Law and all that that entailed. And, we are given the choice to become one of God's own.
In the OT, God communicated directly with people on earth and performed miracles day in and day out for them. And yet they constantly turned to other "gods" for one reason or another. So what makes you think that even if God gave you a direct sign you would then choose to believe that He exists? Because you said so? Well, God said that even if He did give you a sign, you still wouldn't believe. (Mark 8:11, Luke 11:29, Matthew 16:1, Matthew 12:38) So, if there IS a God, would it be fair to assume that we should take His Word over yours?
Of course, we have to make two assumptions: that there is a God, and that the Bible is His Word. You make the general and, quite honestly, cliche, argument that all the crap that happens in the world is in direct correlation with the lack of a loving, caring God. (He is also Holy and Righteous, people so love to 4get those two things in forming their opinion of God, JWs in particular). However, if you actually study what Jesus taught while He was here on earth, you would see that not once does He advocate violence (aka. Koran) or anything else that would be detrimental to society (His people). In fact, He was all for forgiveness (Matthew 18:21&22), love (parable of Good Samaritan, Luke 10), and helping those in need (His entire life was spent doing that). (Btw, as a side note, He also didn't forbid others to preach and heal in His name even if they weren't "with" Him...it's quite interesting, and sad, how many "religions" seem to ignore that little detail) Also, if you study the letters of the disciples, who were directly influenced by Jesus and the example He set, you'll see that neither did they advocate anything that was detrimental, but advocated living peaceably with all, among other virtues. However, how many people actually listen to and apply those teachings (the Golden Rule sums it all up quite nicely, IMO) in their lives? Not too many. Can you not see that if everybody actually followed the example Jesus set how much better the world would be? Even in the Bible, either when God was communicating directly with people or when He was walking this earth as a man, not very many actually followed the desires of God. What assumption can we make from that? That we all have a choice to follow God and His desires or to follow our own will, aka free will. And as we see each and everyday, there are those have chosen to believe in God and try to follow the example that Jesus set (it's not easy at times, trust me), and there are those that follow their own will (while this is a lot easier, we can see how much pain and suffering it has caused in the world).
Now, you can also argue about all those religious wars and the pain and suffering they have caused? That's true, but that's man taking things into his control (thanks to free will) and doing what he wants, using God as an excuse; aka muslims and other radical offshoots of countless "religions". But you say, what about the OT, God was constantly having His people destroy those that worshipped false gods. Ahh, but that was the OT while the Law was still in effect, and while God only had his chosen people, the Jews. As soon as Christ came to earth and the dispensation of Grace began, do you see the need for God to advocate such tactics? No, because now everybody, not just the Jews, are His people, and what would be the point of destroying His own?
True, we don't know what was going on before God created the universe. However, we don't know that the Big Bang happened either (it's only a theory), so why did you state that like it was fact? One common answer I've heard (and find quite humorous) is that God was creating Hell for those who seeked to meddle in things beyond their comprehension. (A little comic-relief never hurt anybody, right? )
That's all I have for the moment. Sorry I have to make the assumption that there is a God and that the Bible is His Word. But isn't that what logic is? Making assumptions and logically reasoning why those assumptions are true? Otherwise, what's the point of using logic to prove something that is already fact? Also, I don't recall the use of fact (that seems more along the lines of the scientific method) every being a focal point in logic, but I may be wrong there.
Btw, don't judge what the Bible says off of JW interpretations...or mine for that matter. Develop your own interpretations...preferably not that it's all crap b4 you've made an honest attempt at it.