In Robo Rally, what happens to locked registers if I power up with more than 4 damage?
They're programmed randomly. This is dealt with explicitly on page 10 of the rules:

LOCKING REGISTERS DURING POWER DOWN
Because robots can still be damaged during a power down, they can sometimes accumulate Damage tokens for a register to lock up before they reenter play. Registers that become locked when your robot is powered down are immediately programmed randomly: Draw a card from the top of the deck and put it in that register, face up.