IPhone 3Gs won't turn on!

My IPhone 3Gs ran out of batteries. When I plug it in, the charging symbol comes on, then the apple logo appears for a while but then instead of the home screen showing up it always turns off again and it shows me the charging symbol again. I have tried pressing the home and power button at the same time but it doesn't work. What should I do? I read something about restoring it but since it doesn't turn on and connect to itunes that doesn't work. Has anyone had the same problem?