I'm old enough to remember when F1 was worth watching back in the 80's and early 90's. To be honest I only watch it now if I've not got anything better to do or it's raining. A complete an utter farse
Have to tried opening both doors and seeing what happens. Also is the boot light working? If no lights are working it could be a fuse, otherwise likely to be either a bulb or the door switch.
So long as you feed in the power progessively and not just stamp on the throttle in the lower gears you should be fine. And don't switch the TCS off until you feel confident and only then in the dry.