Could be *anything*, and that sucks. However, unless you've installed new drivers recently, it's probably a hardware issue.
Carefully clean all the dust and cat hair out of your system. Do this BEFORE moving to the following steps.
Open your box and remove the sound card, video card, and RAM sticks. Check for obvious damage (burn marks). Smell the cards and see if anything smells burned. If not, clean the contacts (a pencil eraser is good for this), make sure you clean all the eraser smegma off, and re-insert the cards.
Remove the HSF, clean the surface of the cpu and HSF off (and blow the dust out from between the fins), re-apply some thermal compound, and reinstall the HSF.
Remove the PSU and blow the dust out of it. Reinstall.
Leave the cover off the box, and turn it back on. Make sure all the fans spin up (including the one in your PSU if it has one). This should eliminate the possibility of heat-related issues.
If the screeching and lock-up still occurs, some piece of hardware in your system has gone south on you, but it *could be any component*.
