Liberty, first let me address your points. As for the origin of the universe, I would agree with you that the Bible tells us that God is eternal, that he has always been. Based upon a belief in the Bible therefore he had no beginning. I don't expect you to agree with that, but that is a Christian perspective. From a scientific perspective to stay within the realm of our understanding, the materials to create the Big Bang must have come from somewhere, because science tells us that something cannot come from nothing. We don't know the answer to that question scientifically yet, so to reject God based upon science, you are placing your belief in an unknown.
Your thoughts on the flood as being a reason to reject the entire bible are interesting. The creation and the flood account comprise the first nine chpaters of the first book of the Bible. Whether they are to be taken literally or not is really a matter of our understanding. Suppose God never meant the accounts to be taken literally and that as Abbaddon puts it, he made it simple so Bronze Age Goatherders could understand it. Does the fact that these stories should not be taken literally mean that the events never happened, or is that really a problem of our lack of understanding? And is this lack of understanding a reason to reject the entire Bible and all that it teaches?
As for the tower of Babel, the problem there was not really the heighth of the tower and I am not sure that the tower is ever described as to a particular height. Nor does the Bible say that God was scared of the tower or of man. It was really a question of man's pride and lack of trust in God that was the issue.
The chronolgy you mention can really only go back so far. The first "seven days" are unkown as to how long they really were. Again that is a question of literal or not literal interpretation.
As for your comments that God should call down from the heavens and tell everyone that he is here, that would destroy the need for faith. And even if he did, those who did not hear it would question whether it happened. I contend that God has made his presence known through out the ages and the message of salvation is known. You clearly know it, but have chosen not to beleive it. So it is not a matter of lack of knowledge.