Put your ear right next to the powersupply. I bet it's coming from there. If so then here is why. You power supply wants pur sign wave power. The ac outlet only provides square wave i think. This causes the ringing in the PSU. Really it's always there but it drowned out when it's on. What you can do is buy a nice APC battery backup. Make sure it's the kind that provides pure sign wave to the pc. This should stop the ringing. my wifes computer has this same high pich faint ringing. More of a constan whine or nails on a chalkboard sound.
Some of the major brand PSU makers are doing this. I belive all thermaltake for sure and hit and miss on the other brand names.
^I agree. It could also be the capacitors on the PSU that make that noise when they are charged. But in that case, the sound is more of a whining, not a ringing.
I also once had a monitor that made this sort of noise. Unpluging it before going to sleep solved the problem.