Common error amongst these iPods, the magic trick is getting it into service mode. Youtube videos are plenty online: http://www.youtube.com/watch?v=SsWgCLAvt...
Basically connect iPod to Mac / PC, hold menu + enter till restart, then do the same again but before the apple logo (with black background, not the faded grey) quickly switch and hold menu + backward (left), until the service mode appears.
Run all the tests automatically (note: some require interaction), when service test is done, just restart again (menu + enter) while connected to Mac / PC, and wait for it to get recognized by the computer.
(This is especially useful, once the battery is sort of completely empty, doesn't matter how long the iPod has been laying in the dust while turned on.)
+ nice description of your actions on the comment