Have you tried a different battery? Asking because of the bit about light on without a battery and no life with. That may indicate the battery is short-circuited or some such.

Yes, there is a fuse. I can't recall where exactly but I do remember it is an SMT component soldered in and not easily replaced. Try a forum search. However the fuse is unlikely to blow unless you feed the USB port with a high voltage. Your symptoms do not indicate a blown fuse.