Thanks Wodrick - your post was really helpful in increasing our understanding!
So far, there's been a growing body of "evidence" (read speculation!) that seemed to point to the aircraft thinking it was in the air when it was not (RAT heater energised, TOCW inoperative). RAT heater C/B was pulled eliminating an obvious symptom but not the cause.
Only problem with that theory - the data recorders showed the nosewheel switch toggling between ground and air mode on rotation. So the nosewheel at least knew the plane was on the ground.
What Wodrick has pointed out is that the nosewheel switch could have been OK, but it was the relay that had failed - leading to RAT heater on and TOCW off, as observed. Plus, because there are 11 relays in parallel off this switch, all other ground/air functions (except AC crosstie and Radio Rack cooling off the same relay) would have been OK.
And a relay failing de-energised is a distinct possibility - coil going open circuit. And it could have happened any time after the TOCW was tested (presumably) in Barcelona.