To avoid going in great length, for this is very benign matter.
General rule is always to isolate the problem source, you obviously know yours.
Unless you made to general description and failed to mention there is (always is) also prior power on on your machine as well?
Machine alone if in overloaded socket might create such anomaly.
PC is really office machine, not purist, dedicated audio machine.
Isolate power socket where you have your computer hardware and remove all audio on different ones, if you can dedicate single dedicated sockets specially for audio even better.
Or simply, take one long cable with enough sockets from different room that is not already compromised with load from PC.
Or you could simply purchase better audio power conditioner like one of these :
http://www.audioadvisor.com/store/categorylisting.asp?hdnCat=Power+Conditioners&sel=1&CategoryID=25
This is just example you can go much cheaper or for High-End much higher.
But power conditioner is something to be inside any responsible (if quality of signal is important) studio or home setup.
You also said nothing about size or model of your screen?
There could be in cheaper models poor isolation and too close near (I doubt) speakers, still capable of creating such delicate but still enough to be heard higher frequency noise.
