This has been known for a long time. The charge to replace the batteries is about $250. Only Apple can do so.
Seems like someone had an external battery device you could plug into the 'charger' port. I don't recall who that was. But that required carrying around the Ipod and the battery device.
Well, no. If you send it back to Apple, it costs $99 -- but there are ways to do it yourself for far less money.