What happens if a powered-down robot sustains enough damage to lock a register (or if it has a register locked through Fire Control)?
Officially, when you announce you will power down, you keep your program cards at the end of that turn instead of returning them to the deck to be shuffled. This is an actual modification to the rules. Any registers that become locked while the robot is powered down with thus have a program card ready. Unofficially, you could treat the locked register as being “unprogrammed”. No card is placed in the unprogrammed locked register phase, and the robot neither moves nor rotates during that phase. Not explicit in the rules, but not a modification either. (This answer suggested by Nathan Sanders.