iPod starts for a few seconds and immediately turns off again?
My iPod is almost completely non-original now. At first I thought the logic board was bad, so I replaced it. At that point it would come on when plugged in, but the lock symbol was on and the click wheel would not respond, even when the hold switch was off. I figured no biggie, since I control it through my car stereo anyway.
"This is likely a battery issue. I have the same iPod (minus U2) and everytime I go to dust it off after months of no use it does this exact thing too.
What I believe is happening is that the iPod battery (when it is fully discharged and/or no longer holds charges) is drawing more than what the drive needs to spin at full speed. My iPod does this but eventually after 10-20 restarts the battery gets enough of a charge to maintain power and the iPod starts up. It could be that your battery is so far gone that this will not happen, and in which case you should buy one of the batteries for 4th gen iPods.
I had the same problem after replacing the iPod Gen 4 battery with a new one. The hard drive would start up, shut down and give a battery low power error message. The iPod case got hot during this process. I plugged the iPod into a Memorex iTrex player and the iPod started up, could play music and the battery began charging normally. I let the iPod fully charge, then ran it down almost to fully discharged. I have since been using the Apple AC adapter and the iPod is now charging normally again.