We're lucky we get a partial damage report, in WWII pilots didn't know the full extent of the damage until their crew chief looked at the aircraft.
If you're engine is shot or not producing power, what do you think keeps enough hydraulic pressure for the brakes to work? On Russian planes they used pneumatic brakes, so even with engine off your brakes would work.
Best technique for stopping quick on the runway, land at 100-120 speed full flaps, after touchdown raise your flaps, this will make your braking more effective, if everything else fails do a groundloop on runway (This is easy to do on a Corsair), let go of the stick and push the rudder to full left or full right, you'll stop quickly that way.