Humming noise follow up

I'm fairly sure this is a power supply problem; less likely, a shorted power output stage which may be a largish integrated circuit; this last one would probably be costly to replace.
A failed diode or filter capacitor in the supply can cause this by either (the diode) allowing unrectified AC to pass or (the capacitor) poor DC filtering of the rectified AC. Neither of these parts is expensive.
Diodes can be in a variety of different packages so giving guidance on these is tough. Capacitors of the type likely used as the main filters in your power supply will be cylindrical objects between 1/2" (12-13mm) to 1 1/2" (~37mm) in diameter and between 1/2" to 3" (~75mm) tall. Caps are in aluminum cases with shrink wrap that will have values given in microfarads (µF) and VDC (Volts DC). Often, when they fail, the exposed tops will bulge visibly as a sign of their failure and sometimes they will leak from the bottom rubber seal and there will be traces of a white deposit on the board around them. If you see such signs, replace them.        
Checking power supply diodes could be done with any multimeter but unless the electrolytic capacitor(s) fails catastrophically as above, the main filter caps would need to be verified for value and losses with a capacitance meter which is too expensive to buy for home use. A plain-jane digital multimeter can cost <$20 US and would be useful for many other tests around your home and car as well.