Power cords themselves won't cause this except that they are the path to ground. So lifting the ground on one or both is another test. Use a cheater plug to test this. Then if that doesn't work I would try the Allnic somewhere else, another system, anything at all just to rule it out.
Solving puzzles over the internet is a PITA because things that would be freaking obvious in person come in dribs and drabs online. Like I just noticed you said "high buzzing comes from the right side of the turntable." What are you talking about? Please be careful to discern between mechanical vibrations you hear emanating from the physical device itself and hum or other noise that is in the electrical signal and so is only heard coming from the speakers.