It is a similar problem in that both problems are EMI related, but what you experienced is noise being transmitted through USB. It's slightly different. I'm guessing that you're not hearing it through the headset once you use a separate USB power, so it's not affecting the sound card or onboard audio, whichever you are using.
As I said above, EMI is the bane of PC sound devices, and can affect sound cards, onboard audio and USB. It can affect one or the other, all of them or none at all.
OP could try a USB sound card, such as the U7 rids57 suggested. That may fare better because being outside the PC case, it's away from the electrical noise inside the case.
If the noise is affecting USB audio as well, then a DAC connected via optical is really the only solution. They are stereo only, so not much use for anyone with surround set ups. Fiber optic uses light pulses, so there is no copper cable that the noise can pass along.