It sounds like the battery is almost dead. Mine was doing the same thing and I eventually found out that the battery needed to be replaced. If you are handy with a soldering iron you can get a new battery for under ten bucks and replace it yourself. If you can’t solder these guys will do it for $20 plus shipping.

I have done both and wouldn’t recommend doing it yourself. And how old is the iPod? The batteries usually hold up for a few years.

Check to see if the cable you are using is capable of charging. Some cables charge, some sync/connect to a computer & some cables can do both.