I have a third generation 15GB iPod. One day I left it in my car, and it was moderately cold out, but nothing to where I was concerned about it -- the iPod was only in there for 15 minutes. But when I went to use it, it was dead. So I tried the various restart mechanisms that I'm aware of, and none of them worked. I tried to reset it numerous times, but it was crashed even harder than the usual crash (probably hardware vs. software).
Three weeks later, I bring it into an Apple store just to see what they have to say, and of course it powered on once the tech plugged it into a power source. And then of course he says "oh, it looks like it's working fine."
So the fix was to let the iPod sit for however long it takes for the clock to drain a fully charged battery (about a week?), then it will power itself completely off. Better than trying to take it apart and unplug the battery -- whoever in their crazy mind would do that?
[robg adds: Leaving a stuck iPod unplugged for a while may or may not help. As a method of last resort, it's certainly worth a shot, though.]
Mac OS X Hints
http://hints.macworld.com/article.php?story=20051108161558461