How to shut down a frozen iPod that's constantly spinning?

I have a 3rd generation iPod that is frozen with the Apple symbol in the window and the sound of a constantly spinning hard drive. I've tried pressing the menu and play buttons to reset it multiple times -- it just blinks and goes back to the same state. Now I can't even shut the thing down -- it looks like it'll keep spinning the drive until the battery runs out.

The iPod does not show up in iTunes or on the desktop when plugged in to a computer.

Any ideas of other ways to shut it down?

And any thoughts about what's wrong? I'm guessing a bad hard drive, although that seems a bit strange since the machine's basically been sitting on a shelf since it was bought and hasn't received any whacks to speak of.