if all that is wrong is the battery, you can or you can have someone replace it for less than a new one will cost.
https://everymac.com/systems/apple/ipod/ipod-troubleshooting-repair-faq/ipod-nano-how-to-replace-battery-instructions.html#:~:text=If%20it%20is%20out%20of,%2459%20plus%20US%246.95%20shipping.