I understand your desperation. It caused me to go back and double-check my previous statements, based on a discovery long ago. My camera is an early SL1. It does have a small (4x7 mm) rectangular switch centered between the rubber part of the eyecup ...
As I wrote initially, on my Rebel there was a tiny unmarked square switch between the hot shoe and the eye cup. I had somehow pushed it when the eye cup shifted. The result was a black screen. Pushing it turned the screen on again. That's just my exp...
I report that without the info above I could have looked forever to find the tiny unmarked square between the eyecup and the hot shoe. And who would ever figure that it turns off the screen? Mine is an SL1. The design is like an adventure game.