See the black wire on the right? It looks like it used to connect to the little solder blob up to the left of the end of it. The black rectangle with the orange/yellow tape on the end is the battery. It's just floating around in the case not really stuck to anything but sort of restrained by the ribbon cable that goes around to the electronics on the other side of the fitbit.
I've never soldered anything this small... but I'll give it a try.