My old first-generation iPod finally gave up the ghost a few months ago. It showed the Folder-with-a-questionmark icon, no matter what I did. I fully charged it, attempted to restore it, reset it numerous times, all to no avail.
Since I had just purchased an iPhone, I didn't really need it, so I didn't bother to send it in and have it replaced (again!) by Apple.
However, the other day I got around to searching for answers on whether there was a trick to fixing it. Sure enough, there is a great post by Matt Hickey that explains how to fix an iPod that won't boot. Apparently this is usually caused by a hard drive that stops spinning because the metal case has warped.
The first thing you need to do is find a screwdriver or other tool thin enough to loosen the glue and pry open the case. I tried a number of items that were lying around, but didn't make any progress - the case looked as if it had never been touched. The ipod had been face-down on the desk while I was attempting surgery. When I turned it over - surprise! It was back up and running. Apparently the jolts caused by my poking around with nail files and screwdrivers were enough to jar the hard drive back into action.
Take a look at the article if your iPod won't respond to the usual treatments.