The parts are cheap enough and almost surely the problem.
Once you figure out a part number, I'd probably just go ahead and order enough to replace them all.
But if you wanted to do some testing:
Hook up 5v and ground to the appropriate pins.
The IR LEDs located on one side of the black modules should stay on all the time. You can see them through a digital or cell phone camera. (may need to be in a dim room)
Some or all of those being burned out is most likely the problem.
The other side of the black module, opposite the IR LED, is a sensor that acts like an on/off switch and allows power to pass when light hits it. (through a slot in the wheel)
Ambient light from the room can also trigger it.
Each of the sensor pins coming off the PCB should show voltage when the sensor is exposed to bright light and not show voltage when it is covered up.
There were some old games that had this backwards, but same principle. It changes in response to light.
That's all there is to it. Those two pins just output a blip of power whenever the slot in the wheel passes by.
The sensors are staggered in such a way that allows the computer to tell which direction it is spinning and it can tell the speed by how fast the blips are coming.
(All the terms I used here might not be considered technically correct by people with a deeper knowledge of electronics, but I think they work better for explaining things in layman's terms. i.e. someone who knows enough to test for power or continuity, but might not know what is meant by terms like "pulled high". That was me when I first got here.)