Sounds like the display driver. Not seeing the movement the display driver may be a separate chip or built into the main IC. also not knowing the history or age of the watch there may have been damage from out gassing in the old batteries.
It does not appear to be a connection problem at the LCD panel. Check all the traces from the IC/display driver for corrosion which may be confusing the signal as the display driver interprets the digits and send that info to the display.
Cheers, geoff