The problem only occurs when starting certain games, and even then only when certain games are set to certain video settings (for instance, for my WoW 2.4.3 private server client, it only happens when I start it up with everything set to max settings -- and even then, the noise goes away when I actually begin playing. Same for Crysis.)
Every other game I have doesn't cause this odd whining / screeching noise. It's a rather faint sound that only pops up -- and instantly pops up -- when I start the two aforementioned games. Crysis 2, Mass Effect 2 / 3, Starcraft II, Diablo III... Every other game doesn't seem to do this. Any suggestions?
While very odd, I'd still have to say that if you're hearing some kind of mechanical whine or screeching noise from the HDD, then that is a sign you should replace the drive ASAP. It might just be that the data for those programs is physically stored somewhere on the platter that is in a "sweet spot" for the read/write arm. A bit of a stretch, but again the specific reason doesn't really matter. Any abnormal mechanical sounds means replace the drive ASAP.