Are they the right size batteries in there? They appear to be sticking out well from the back of the module, seems to me wrong size batteries have put pressure on the module and that's what has killed the first digit.
Why does someone with your knowledge on digi watches need to go to a jeweller for battery changes? I'd have thought you'd be doing your own, even if you had to buy opening tools etc they'd pay for themselves within a couple of changes with what these jewellers charge.