Dan & Bruce, fair points, but the probability that effects at the inputs are causing the problem would seem to be low given that the hum is insensitive to the volume control setting.
Matt, given your thorough (and excellent) description of the issue, I'm mostly stumped. But to grasp at some straws:
1)Perhaps for some reason the AC safety ground pin on the outlet isn't really grounded. It seems conceivable to me that plugging into an ungrounded outlet could cause these symptoms, especially in the case of a high powered amp such as this one.
If you have a multimeter, see if ~120 volts AC can be measured between the smaller of the two vertical slots on the outlet and the metal in the outlet's safety ground opening.
2)Make sure that the speaker cables are not routed close to and in parallel with any power cords. If they are, 60 Hz EMI could conceivably be coupled into the speaker cables, and from there into the amp's feedback loop.
3)Disconnect power from any other components or electrical devices that are close to the amp, although it sounds like you've already tried that.
4)Try turning off any fluorescent lights, compact fluorescent lights, and dimmer switches that are anywhere in the vicinity.
Hope that helps. Regards,
-- Al