The mouse on my A2000 only moves vertically up & down.
Given the fact that you still have movement, it's unlikely to be a problem with the 5V power supply to the mouse.
More likely to be an issue with the connector, one of the inline ferrite beads or with U202 (8 to 4 line multiplexer). Very quick and easy to trace with an oscilloscope, keep moving the mouse and find where in the circuit the quadrature signal (will appear as a 5V rectangular waveform) stops. Schematics
here.
If you have no horizontal joystick movement in the other port, then the problem is likely to be downstream of U202. In which case look at U4 (Denise) which reads the four multiplexed input lines.
