You may wish to try plugging it into your computer, opening up the Disk Utility app, and see if it shows up in the left hand pane. Go from there - it may be a software issue. My 80 GB 5th Generation iPod Classic showed a dead screen, and now I'm getting a faint 'Please wait - Very low battery' issue on the screen, so it's probably my battery, although I've basically only used it as a storage device - go figure.
I had similar problems with my 17" 1.67 GHz PowerBook (A1107). I would get a start-up whirring, some light flash, and then a power-down with a low hum (meaning that it was still getting power). I also lost my harddrive test CD to the diskdrive. When I took it in to an Apple store, they told me that it was the logic (mother) board and would cost $1,200.00 CAN! I assume that's w/out labour! It makes a helluva platform for my external HD's, iPod dock and external speaker now. Another case of obsolescence built-in. If you know anyone with a good motherboard, please post!