Okay, this is a LAST DITCH SOLUTION. I'm probably gonna get glares for even mentioning it, but it DOES work. Confirm beyond any shadow of a doubt that the HDD is the problem before trying this!
Freezing your hard disk often makes it work just enough for one last gasp. The one time I tried this, it was with a HDD I found at the side of the road (no, really), and I was curious to see what it contained. Plugging it in didn't work, so I tried the freeze trick, and lo and behold, it worked. However, melting frost then shorted the drive and killed it.
I got to play the leaked Doom 3 demo, though.