If it works fine (though laggy) whilst connected to a charger then it’s more or less gotta be the battery. Changing the battery on a iPod is quite difficult, but you can do it if you’re up for a challenge. There’s some chance you could get it running better by wiping it and reinstalling it from scratch. If some of the flash memory cells are beginning to require heavy error correction then that might force it to rewite iOS to less worn out cells.