Have you tried removing and re-seating Denise (U201)? The M0V and M0H signals eventually end up on pin 38 and pin 9 of Denise respectively.
Here's a list of parts that /could/ be suspect, starting at the signal side (joystick port):
Pull-up resistor pack RP200 (bottom left)
Pull-down resistor pack RP205 (bottom left)
Feed resistor pack RP204 (bottom left)
Quad multiplexer U202 (bottom left)
Denise IC U201 (bottom middle)
It's a bit odd that both joysticks work perfectly, though. If you have an oscilloscope, you could try looking for a pulsetrain at pin 38 and pin 9 of Denise (while moving the mouse plugged into port one), and comparing it to pins 9 and 12 of U202 to check if there is a break in the signal path between both ICs