iPod Nano 5th gen only works when docked

I dropped my ipod nano 5th gen. When it is docked, everything works great, but it powers off instantly when unplugged, and when it is re-docked, it boots up as if it shut down due to battery failure. It will then indicate that the battery is charging, but even when I wait until it says the battery is charged, it will still power down when undocked. The battery was in great shape prior to me dropping the thing. Could it be as simple as a loose battery connection, or am I SOL here?