I had this exact problem. Then, the iPod eventually died and would
not restart. Since Apple had such draconian service in the early
days of the iPod it just sat on my desk for a year and three months.
I sent it to iPodMods.com and they were able to fix it. What they
found was that the firewire jack became disconnected so the battery
was never really being charged.
So, see if ipodmods can resurrect it for you.