Help, Strange Static Sound Recurring

This seems a bit of a stretch but since you haven't isolated the source of the problem maybe try switching the speaker cables left side for right to see if somehow you have an intermitent short starting to develop in the speaker wiring or connecting cables and it's affecting a protection circuit in the amp. If the problem switches sides you have a start.

If not, obviously your goal is to isolate their source of the problem. If you have balanced interconnects throughout your system you may be able to carefully disconnect components starting at the Theta transport and working your way toward the speakers. If the noise goes away when you diconnect a component or a cable then you're making progress. Balanced interconnects can also be carefully switched left to right to see if you can get the noise to switch sides.

Hang in their! Remember your experiment is to make only one change at a time.

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.

I think Bob gives good advice. Keep the system. After all, your dad handed this down to you becuase he wanted to share a hobby with you that he enjoys. He could have sold it but he chose to give it to you. Honor that gift and enjoy it.

Is there a Ham Radio operator operating nearby? I had a bad ground going to my system one time and with power turned off I could hear some static and bearly make out a voice. The Ham was totally legal in his transmissions and wnet ut of his way to help me find the bad ground.

Regarding possible service: I know an expert in Minneapolis area that may be able to assist you himself, or can refer you to someone else who can.