PSU TEST:
Ok, well its Pin 16 is the POWER ON line... It was or should be GREEN
Either side of that, PINS 15 and 17 are both GROUND. There are a few grounds, but m,ight as well use the ones next to it... Use a bit of wire or whatever the heck you want, just to force the pwoer supply to power on and if that hums or does the noise, then yeah, its the Power supply, but if its silent, then its not the PSU!
But as you have another PC, then I'd do that method first.
Similarly, just swap the PSUs around if you can and see if either makes the noise!?
Whats the Earth Hum?
Well, its sort of a low sounding MMMMMMM sound, that is sometimes barely noticeable or it could be overwhelming.
You can get it when you use low quality poorly shielded cables.
For example, years ago, I had my music equipment all setup and I had a non-stop buzzing sound that I could not get rid of.
Then, when I decided to go through my wiring again, I found that the LINE-LEVEL cables, or rather a couple of them, were going alongside some MIDI cables. The trouble is, that I used unshielded cabling as I had cut a load of corners, and seperating the cables cured the issue. SILENCE!!!
So, I bought some betetr quality cables with good shielding and the issue was cured full time.
What this was basically caused by, is the noise of electic pulses in the wires were crossing over and affecting the audio.
This is NOT what you have, but it taught me about the importance of good quality cables.
You can also get it with some kind of SHORT. This may be what you have. Perhaps the Motherboard is touching, a part of the case, or there is some short with a peripheral, or anything that is making some kind of connection thats causing it to short somehow? - Of course, I dont know what the cause is, but I have had times when a PC does have a weird noise just like yours, and its been fixed by simply re-seating the Motherboard, and of course adding each part one by one, just in case its something that seems to be nothing to do with the problem, but indirectly is the culprit!
Good luck.