What should I do when I get the "very low battery" message?

I would of course start with he battery and replace it. Check the dock connector (where the cable plus in) make sure that you do not have any bend pins, that there is no corrosion on the connector and that there is no debris inside the connector. When you replace the battery, check the connector itself. It is a little flimsy design and has the tendency of easily breaking of the logic board. If you have a firewire adapter for your iPod you could try to charge your iPod with that since it does supply a little higher amperage. Good Luck