He was administering a damned good thrashing to a stationary car.
Does it mean:
His car broke down and he was trying to express his discontentment by smashing the car?
As I remember the episode, the car was elderly and not running well. When it broke down at an inconvenient moment, it was the last straw for Basil and he sets about thrashing it with a stick.
You are correct, but it is not quite as gentle as "expressing discontent".