Maril,
Wow, I just read through all of this, at Jea's suggestion. Let me make sure I understand what amp we are talking about. If I followed everything correctly, you are having the problem with your friend's pair of BAT VK-150SE's, not the VAC amps that are listed in your system profile. And you previously had (or still have) a BAT VK-75SE (similar to the 150SE but in stereo configuration), and it exhibited similar symptoms.
Do your VAC's have these symptoms as well?
I notice that the BAT amplifiers have a bandwidth spec of 200kHz, which is extremely wide, and approaches rf frequencies. I'm wondering if there may be rf interference coming from somewhere that is radiating directly into internal circuit point(s) within the amp, and somehow then intermodulating or being AM-detected somewhere in the amp circuitry, resulting in the sound you are hearing.
Can you tell if the sound is really 60Hz, together with its 120Hz and possibly 180Hz harmonics (corresponding to the power line frequency and its lower harmonics), or could it be some other frequency or frequencies, which would be suggestive of rfi pickup?
The computer that you mentioned is in the room would certainly be one such possible source. If you haven't already, try turning it off AND unplugging it -- as you probably realize some circuitry on the computer's motherboard, and parts of its switching power supply as well, are always powered up as long as the ac is connected. For that matter, unplug all other computers in the house, and if you have nearby neighbors, consider asking them to do the same.
Perhaps you could bring an AM portable radio into the room, or better yet if possible a portable that can receive the long-wave band (below 550kHz) and see if it picks up any interference. If it does, you could track down the source of the interference by walking around with the radio and seeing where it is loudest.
Also, just to be sure, did the XLR shorting plugs you put on the inputs have all three pins electrically connected together (such as by having pin 2 wired to pin 1 and pin 3 wired to pin 1)?
Regards,
-- Al