I would cold boot to your Windows disc, then run it in R ore Repair Mode just to clean up common Windows defects. Some restore discs and OEM versions will not do this.
How old is your drive, and what is the brand? Have you had any other sorts of problems recently.
Just to set aside nagging problem ideas, I would go to the website of your hard drive manufacturer and download their latest drive fitness test. It will quickly tell you if you have drive problems brewing.
Then, of course you must do system scans for spyware and evil infestations.
Next, I would take a look at the Event Viewer to see what stops and evil failures have been reported... read through the entire list of anything in red. (Control Panel-> Administrative Tools-> Computer Management -> System Tools -> Even Viewer)
Can you describe the screech? Is it coming out of the speakers, or deep in the depths of the computer case?