My wife's iPod broke last year. The hard disk was clicking and the device just wouldn't boot up. We took it to the genius bar and they helpfully suggested we buy a new iPod. Tough break.

Then somehow we found out about this cool the hard disk technique. We put the iPod in a ziplock bag and in the freezer overnight. The device was working perfectly fine while backing it up, but as per the post, it would warm up and start stalling. So we put it on an ice block and it lasted long enough to get the backup done.