What should I do when I have taken my car to a car dealer without any written agreement and the garage owner refuses to give back my car because he insists I owe him rent?

I'd initially report the matter to a non-emergency police phone line, with the view of pressing criminal charges and prosecuting him.

If I understand correctly, it sounds to me like the car dealer has tried to impound your car (the rent charges).

If that's the case, it's something he's not allowed to do without a license anyway. And even then, there are strict guidelines on how things should be handled.

Also, the fact that you don't have a written agreement shouldn't work against you. If the car dealer wants to claim any money against you then the burden is on him to prove that you are liable - not the other way round!