Try unplugging the TV and everything else in sight that could conceivably be generating and radiating RFI/EMI into the amps. The fact that the VAC buzzes when the inputs are unconnected, but does not buzz when the inputs are shorted, may be an indication that the unconnected inputs are picking up some kind of interference that is radiating from some other electronic device. And perhaps the Doshi is picking up the same RFI/EMI at an internal circuit point that is not affected by having its inputs shorted.
Also, if you have a portable battery powered AM radio, set it to an unused frequency near the bottom of the band (e.g., 540 kHz), and if it picks up any audible interference that gets louder and lower at various places in the room, use it to track down the source.
Also, when you find the multimeter run some checks with it on the AC outlets. Set it to measure AC volts, on one of the higher voltage scales. You should measure approximately 120 volts between the two vertical slots in the outlet. You should also measure approximately 120 volts between the smaller of those slots and the screw that holds the wallplate on, and between that smaller slot and the safety ground connection in the receptacle. You should measure close to zero volts between the larger of those slots and the screw that holds the wallplate on, and between that larger slot and the safety ground connection in the receptacle.
Best,
-- Al