Try reboot. Press menu and Center button. do this then run the batteries down all the way, then plug it into the computer. Let charge for an hour and then open up Ipod Restore program and Click the second option RESTORE! DONT UPDATE! NOTICE THIS WILL DELETE EVERYTHING OFF THE IPOD MUSIC AND ALL! After this put a few songs on if they work fine then congrats. Sorry but I am limited on time rite now. I will be more avaible in a few hours though.
Does it make any noise or get very hot. Does it come up with a folder icon and a sad smilie face? If then those are symptons that the ipod is going bad. But dont worry there are ways to fix this.
As I said I will help you out more later on tonite.
*EDIT*
Hopefully this helps you out identifiying your ipod generation I think it might be either a 3 or 4th gen.
http://www.ipodwizard.net/showthread.php?t=2367