Thanks for this.
Does this work for the free version and not the paid one? I ask because I've been exploring for a while and can only find car batteries or bullets (using the explore button)
Yes, they all work in the Free game. The only advantage the supporter code gives is the ability to choose the event, which still doesn't guarantee a car part.
At the top of the left panel is an arrow that points to the left (back button). Press 'Explore', if its not the Police car or the cave, press the back button, and the game will 're roll' the event. Repeat until you get the car or cave with car part.