As I remember, on old day explanation, a person in a car hitting the interior of the car cannot move the car, because there is no action and reaction force between the car and ground. But I doubt the car can move actually because:
When the person starts to extend the arm, due to conservation of momentum between arm and car, the car moves to the opposite direction of arms
When the arm actually hits the interior, the arm stops, and due to conservation of momentum, the car stops.
In the time between the person starts extending the arm until the arm hits the car, the car has displacement
So I think if the person hits the car and don't retract the arm, the car would have net movement, am I correct?