Not working, but working?

Hi-found an unused Ipod nano 4th generation in a drawer; plugged into pc & it works, connects and syncs, but thats it; when its unplugged, menu flashes for a second, and turns black...brought it to the genius bar: when they plug it in, its fine, you can go through the whole menu, unplugged its blank again...any ideas on how to fix it? brand new, hate to dump it -thankyou