Help, Strange Static Sound Recurring

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.

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.

Hy there's one other very basic issue that I forgot to mention, which could be the cause of this intermittent noise. We sometimes "look too deeply" into a technical problem, neglecting the basics which those of us that are more-experienced tend to take for granted.
This very basic issue is cable contact cleaning. As you are new to this, I'll explain again briefly here & then drop in the link to Galen Carol Audio's excellent website; under the "archives" section are many tech. tips that you should become more familiar with. Look over his whole website, read & learn a lot!
What happens over time is that your interconnect cable ends, panel-mounted equipment jacks, speaker cable connectors & ends attract dust, dirt, oils from skin contact, metallic oxidation occurs. This contamination causes (1) sonic degradation (2) possibly noisy connections esp. at the signal-interconnect level. One of the best & most popular contact cleaners is a product called Kontact, widely available, & one of Galen's favorites as well. If you're hesitant to spring for a $40 bottle of this "magic sauce" then at least get a small container of pure denatured alcohol from the drugstore; do not use isopropyl alcohol etc. as it contains lanolin, an oil which attracts dust right back into the connections, and water among other contaminants.
Cut some pipe cleaners into 1/3 sections & use those as your mildly abrasive applicators. Dip into the solvent & then scrub the cable connectors clean, both inside the contact point tips & around the shields. Also go around the outers & inners of your components' jacks, first ensuring that power is turned off. Also clean your AC cords, the mating female IEC's, speaker output posts, posts on the speakers themselves, & speaker cable ends. Change applicators when they become dirty looking & be sure to do that critical "second cleaning" as Galen explains all in great detail. If your intermittent noise is related to dirty contacts then this should fix that, & even if not then you'll still benefit from sonic improvements that can sometimes be dramatic in cases of gross neglect.
Here's that link:
http://www.gcaudio.com/Archives/howto.html

Hy I noted your query above. By removing the input cables from the amp, then powering back on & just letting it sit idle, have you definitely isolated the intermittent to the amp itself? I'll send you a separate email with the requested info.