Hy whatever you do don't listen to your wife - she has not the slightest appreciation for what you have there, which is a very nice rig esp. for a newbie. Beside that, someone else will end up with a steal of a deal on this equipment & then go have it fixed anyway, & you will not be able to sell bad equipment for a decent recovery price.
You seem to have an intermittent connection in the power amp. The suggestion to reverse speaker cables is a good one; you could swap the input cables at the same time to keep left = left etc. The UPS experiment was indeed worthwhile to eliminate a possible line-voltage problem situation; however while a computer UPS is not the best from an audio sonic standpoint (the output waveforms aren't very clean) it shouldn't have hurt anything, & was a good thing to try from a troubleshooting perspective.
Focus closer on the Rowland; leave it powered on with no inputs connected (for however long it usually takes) to see if it noises up again. It could even be just a bad input cable connector that is causing this. Indeed, only make one change at a time, pursuing a process of elimination, or else you'll really confuse yourself.
If it is for sure the amp itself, then the intermittent connection is probably clearing up as the unit is moved around, shipped, etc. Then it reverts to intermittent/noisy again after settling awhile. It could even be the AC switch but this would probably affect both channels? It could be a dirty wiring connector or a PC board edge-connector inside, it could be an old cold solder joint or solder bridge on a PC board. This will take some time & patience from an experienced & knowledgable tech. but it can be found; I do this for a living in the Telecommunications business & can fix many things that others can never find. Shoot me an email inquiry with phone contact if you'd like to discuss in detail some evening.