Being possessed, the exorcism is probably a good place to start.
Is it a climate control system, or the manual unit? It could be something like a loose plug, bad brushes in the blower motor, etc.
Usually a failing blower motor when stopped will spring back to life when tapped . That gives you a place to start. When it acts up, start fiddling until it starts working. Of course being intermittent however, the issue will only present itself when you do not have time to fiddle.