Although the charger may be working, have you also checked the cable that connects the two things together?
One thing that tends to happen with this type of cable is that the sheath splits and you can see the inner coloured sheaths of the individual wires. In my experience, this can hide the fact that one or more of those wires is no longer working. Typically, the connection between the wire and the plug pin becomes detached because the outer sheath, which acts as a strain relief to prevent the wire becoming detached, is no longer effective. Do you know anyone with a cable that you can try as a test?
Another thing to consider is debris in the iPod's connection socket. Use a very gentle brush to remove any fluff or lint. It might be a good idea to confirm that there's no debris in the connector on the end of the cable too.