I think you miss the point of the laundry list of miracles of Jesus. Magic was more common then we think and in this time there were other cases of the dead being raised, things Jesus did himself. These miracles were not atypical. These were primitive people.
The question asked is really a modern one. We don't even know if Jesus existed yet we automatically take it ture because the Bible says so. For whatever reason Man has a need for God, it's that simple.
We believe in the New Testament because we believe in the Old Testament, just as the Muslims believe in the Koran, because there was a Torah. Everything is relational. I know we don't like hearing this. If there was no Judaism there would be no Christianity or Islam. Notice mankind was not able to go beyond the precept of God once it was established.
Yahweh, Jesus, Allah are all the same and fill a need we have. They give us purpose, peace (at least suppose to), insight, and fulfill us spiritually, but appartently not insight. In every religion we have strayed. I've always wondered if we could prove one religious idea was wrong, then would the other give in and follow. Religion reflects society. The more stable the society the more open the religion will be (with bias of course).
I really hesitate to try proving a specific (national) God doesn't exist becuase I don't think man could handle it. I think many people just would not be able to cope with that, to the point the world would come crashing down around us, it's just that serious.
I think Jesus has the element that allows us to approach God. He is a step back in time. The plausibility of God incarnate has to be taken real as the OT gives evidence of personal God that manifested himself physically several times. This came to be reinterpreted over time as incorrect to the point if you came in contact with God you would die. God once walked the earth, and was the type of God that sat down and eat a meal with us to becoming being comic and unapproachable. God can't be that elevated. At one time we could touch him to not being able to. Jesus humanizes God once again and hence why he is personal. To us that has become and is important, to other cultures that apparently is not important and they want this unapproachable non-personal God. I hate to classify this as political and societal but that's what it is.
All religions I think carry God too far.
