I considered it a while back and did some research. If you send it in to Apple, you don't get the same pod back, they send you an equivalent one (which makes me cringe, thinking of the number of people who pick their noses). Also, if your iPod is personalized with engraving or something, you lose that. Depending on your model, it will cost anywhere between $50 to $80 bucks.
I know there is a YouTube video out there, showing you how to replace the battery (which is easily available on eBay) but I watched it and it looked too complicated for me. My husband probably would have been able to do it.
Have you checked Apple's troubleshooting page for charging iPods?