Simon nailed it. The thin metal strip sticking up from the watch circuit board touches the watch back but needs to be isolated from the battery. If the clear plastic cover is still on the battery holder, make sure the white tab sticks down between the thin metal strip and the battery holder. (Believe you could also use a piece of cellophane tape.) I had the same problem and that solved it.
I don't believe you'll find an exact replacement for the watchband. But I found a black 18mm sport rubber watchband that attaches perfectly to the Adidas logo piece and the white striped piece on the top and bottom of the watch. Part MS934RA18 from www.jewelryservice.com. Five years ago it was $14.95.
mark
October 2014