On one hand, the fact that you say the drive is making a 'whistling' noise and the computer is so unresponsive makes me think that the drive could be dying. But because you have stated that it only happens when the computer is idle, it seems that it could be a scheduled task set to run at a certain time or when the computer is not in use. Are you sure your virus scanner is not doing doing scheduled scans when it happens?
Next time it happens, I suggest you try to open the Task Manager to see if you can spot a process that is using a lot of CPU time and accessing the disk. Be sure to click the Show processes from all users button. Also try to find out if there is a pattern to when it occurs, e.g. does it occur almost exactly two hours after you last used the computer.
It would be useful to know if the activity stops shortly after you press a key or move the mouse. If so then it further suggests that a scheduled task is set to run only when the computer is idle. There are a few programs set to run like this, e.g. the Windows performance monitoring tool, but none I can think of that run that regularly. It is possible to view scheduled tasks using Start -> Run -> taskschd.msc. The program gives a list of tasks that have run recently, but finding the relevant one may not be easy.
Whilst it could be that search indexing is causing this, it does not normally cause a problem as it is designed to run in the background without harming performance significantly. The simplest way to rule out the indexing service is to temporarily disable it.
If you're still having the same symptoms it could be a problem with the drive itself. I suggest you download SpeedFan and check the S.M.A.R.T data for errors. There are also some tests in the program that you can run manually. It could also be useful to run chkdsk (accessible by right-clicking the drive in My Computer and clicking the Tools tab, then Check now...) as you may have some bad sectors. In the mean time, be sure to have a backup of all your important data.
Lastly if you still have no leads then I wonder if malware could cause this. Specifically, a rootkit that's up to no good and able to hide its activity in Windows. What kind of malware protection do you have?