I have the same problem, I post it here: Why my iPhone does not finnish the starting up? If you have founded any solution to it, I would so appreciate if you could share it with me.
I have a similar problem. the battery died and when I tried to restart it, all it does is showing me the apple sign, but it does not go further. I can't start/restart it, and I can not restore it because iTunes wont recognize it until it starts. If I find any solution I will post it to you too, you might be able to use it. Blessings!