Backup important files just in case it is your HD.
Clean all the dust out of your machine, including heatsinks, fans, and case filters. A can of compressed air should do the trick.
Run your computer with the case opened. Try to reproduce the sound and listen for the malfunctioning fan(s). Replace it.
It is likely just a fan. Usually "high pitched whine" means a smaller fan. Possibly on your video card or motherboard chipset. Maybe on your CPU heatsink.
My parents computer has this earsplitting super high pitched ring or whine coming out of it. The sound is barely audible because the pitch is so high but it is definetly there.
At first I though the fans need to be cleaned because it is just dust or something, but I noticed that whenever I minimize all of my windows the whine disappears or goes much quieter. This seems to be most evident when I am running Firefox. (I havent checked with IE).
Sometimes the whine mysteriously stops and then starts up again for what seems to be no connection to anythng.
Is this perhaps the processor suddenly screaming at me, or perhaps a magnetic or interference problem with my high speed internet?
I am not on wifi. The hispeed internet has been in there for at least 16 months and is built into the motherboard.
Dell Dimension 2400 p4 2.80
Pretty much still factory defualt still.