This might sound an odd question, but have you tried looking at the sensor bar through your phone? Most phone cameras don't filter out infrared light, and so you can use that method to see if things like TV remotes are dead. The Wii "sensor" bar is really just a fancy case that houses a load of infrared LEDs (see the image below, taken with an infrared sensitive camera). It should look like that on your phone, if it's powered.
The actual light sensors are behind the black panels on the top of each wiimote.
On the same note, if there were other sources of infrared light in the room, that could conceivably cause problems. It is the case that the Xbox has an infrared LED ("blaster") of its own:
You didn't mention a kinect, but if you have one attached to your Xbox then it's also worth noting they work by flooding the room with infrared Iight and measuring it as it reflects back, off of other objects.
You mentored that powering off the Xbox didn't help, and realistically it shouldn't be shooting out light unless you're using it at the time. But it's not a crazy idea by any means. In fact, it could even be that there's a mirror in your room that's causing problems. I once heard a reviewer of a VR headset that couldn't get their system to work, until finally realising it was the fault of their full-wall mirror.