You've done the right thing and ruled out problems with the casing or the external part of the switch (the plastic button cap), and now we're down to problems with the switch, the circuit traces, the electronics, or software.

Just for the heck of it, see if a paperclip reset fixes the issue.

If I understand things correctly, isn't there a small amount of soldering required to replace the battery? Maybe something happened there like a tiny dropped solder blob or something, that now needs to be scraped off the circuit board.