Google how optical encoders work. The info is in some threads around here, but I can't seem to find them.
Basically, you only have power and ground going to a pair of emitters (infrared LEDs on modern stuff), and then power going into the optical sensors and "output" (or "data") coming out of each sensor. The sensors are just optical on/off switches. They allow power to pass when light from the emitters hits them.
They are spaced so the pulses of output A and output B create a different pattern of pulses depending on which direction the wheel is spinning.
I haven't messed with old arcade wheels as much as other stuff, but you can usually test IR emitters by looking at them through a camera.
Make sure they're both lit up to the same brightness as the ones on the working wheels. They should be fully lit all the time. If they go out or dim, something is wrong.
Use a volt meter to make sure the sensors are putting out full voltage when triggered (I'm guessing 5v).
Test voltage going into the board for that matter.
If any of the emitters or sensors is bad, replace them.
Just cleaning them might help. If either an emitter or sensor is dirty, it will have a harder time doing its job.
If any of them have been bumped and is not pointed in the right direction, that would also have an effect.
One other thing....bright light from other sources can also trigger the sensors when they shouldn't be triggered.
Has that particular wheel been modified in any way that would allow light from the screen to bleed into the area where the sensors are?
Could be that the upgrade screen is just brighter enough than the others to mess it up?