My best bet would be that your battery is dead. Batteries needed to be used otherwise they die. As for the charger, it's probably like my N900, it could be on charger, but still runs off the battery regardless. Being said that the the best things you could do to confirm:
1.) Either borrow an N800 compatible battery and see if it works.
2.) Or take the battery itself to a sparky(or a friend who is into electrics) who can measure it if it's really dead. If so just buy a replacement battery.