Today I unplugged a power chair in the living room and plugged it back in to the same outlet. The light on the other side of the living room on a different outlet went out and would not work again afterwards. I checked the fuse box and no breakers were off. I am perplexed.

Remove one of the outlets and see if it was wired using the "Quick Connect" holes in the back. These are known to develop poor connections over a period. The poor connection can be at the last working outlet or the first non-working outlet and can be in the hot or the neutral side. If the quick connects were used, rewire all the outlets and switches on that circuit using the screw terminals. If you were to find and fix this specific poor connection, it will only be a matter of time before another one develops at some other place.
After you have rewired all the outlets on this circuit and developed some confidence, rewire all the outlets in your home.

Patricia, Harold gave good advice but I'm curious, when you say no breakers were off, did you just look at them? I would throw the breaker switch and reset them manually. Sometimes breakers can appear to on. Good luck