Problem solved thanks to Canis. The trick is to install the iPod updater software in Windows. Reboot the PC (as requested by the installer). Run the iPod updater and plug the iPod in. Restore it (note that it will wipe everything on it) and plug into the mains charger as per the instructions in the installer. Once it’s rebooted, check that both the PC and the mac can talk to it and that’s it. Job done.