iPod nano only works when plugged in?

i have a gray iPod nano, 4gb with colour screen and a click wheel. It lights up, and can play and move music--but only when plugged in. When it is unplugged it turns off immediately. It says that it has a full charge, but as soon as i eject it the iPod turns off instantly. When i plug it back in it reboots (i see the apple logo).

any ideas?