My I pod nano 3g only switches on when adaptor plugged into mains when I take the adaptor out and put the headphones in it will not switch on.

The battery is probably dead. You could try resetting first by pressing the menu and center button for several seconds while toggling the hold button.

You can also try restoring it by downloading the appropriate software for your model which can set it back to the factory settings.

If none of that works, your battery is most likely dead and needs to be replaced. You can try calling Apple customer support to see if it can be replaced under warranty.