I agree with Jeff who has made a pertinent point -- sometimes more context has to be given when homonyms are involved. Your sentence: "The police fined me while my car parked in the middle of a street." sounds a little incomplete to me as I would be wondering if the car parked itself in the middle of a street. Perhaps you can write: The police fined me as my car was parked in the middle of a street. In this case, your use of "was parked" is the passive voice and the reader can infer easily that someone (you) parked it. You can also write: The police issued me a ticket as my car was parked in the middle of a street.

in this case I will change a little bit the expresion: The police give me a fine because I did park it in the middle of the street

Yes. It is understood because of the other meaning of "fine". It is not ambiguous because of the given context. However, the following sentences are ambiguous without more context given. Singapore is a fine city - a nice city or a place where you get fined easily? The queen threw a ball - did the queen throw a party or did she really throw a ball?

I would say 'The police fined me while my car was parked in the middle of the street' but i am not sure if you meant 'The police fined me because my car was parked in the middle of the street'.