I think Konky has a good idea. But I think Dave in Decatur also has a point.

I've seen some wierd stuff when batteries are over-charged, or batteries are undercharged, and it could be the AC Adapter was (is) at fault, and the phone is trying to protect itself.

I'd go to a corporate store and ask them to try a new battery and another charger and see if after 20min of charging the new battery, if the device behavior is different.

THEN, if that didn't work, I would go the FDR route, but I would have someone in a corporate store see that you performed a wipe and the device is still wacked, because at that point, I think a replacement device is in order.