Back in 2012, I purchased an APC RS1500 UPS for $20. The guy I got it from could not get it to work and said APC tech support told him that his house wiring was to blame. This was right up my alley!
After running a few tests, it was apparent that it would not stay on-line, switching to battery mode randomly. I could see why tech support suspected a noisy line supply. However, putting my scope on the input, it was clear that the line supply was very clean: the first clue.