I will agree that iPod batteries are challenging, and if it is more than what you want to tackle it might be a good idea to take it to an expert.
Does the device turn on at all?
If so, you can sync your iPod with iTunes on your computer to back it up.
If you decide to get a new Apple device like another iPod or an iPhone, you can load the backup to the new device to transfer all of your info and playlists.
https://support.apple.com/itunes