my ipod does not work when not plugged in

Does anyone have suggestions for the iPod Classic. When it is plugged in to power source it works fine. When I unplug it, nothing. When I plug it in to the computer still nothing but it does say "very low battery" and the battery is fully charged. Also, iTunes does not recognize the device and it does not show up at all.

I know, lots of problems. I have tried to reset it as well. Still no luck. Any help is appreciated.