It seems that people think your car is abandoned or is undriveable and is taking up space on a public street. I would simply suggest that you don't park your car in the same place all the time and maybe even move it every few days. Most likely, it was a neighbor who reported it. (I've done that before). Most cops don't have time to go around keeping track of all the cars on the street. You might even write a letter to the local police dept. telling them of the situation or file a complaint.
As for your $300, you'd probably have to sue the city to get it back.
Does the parking ticket have the date it was issued on it? If not, tell that to the judge for an easy dismissal.
You need to tel the powers that be your story/information and make sure they know all of this so that you don't get ticketed or fined. You are doing what you need to, now make sure the correct people are hearing it.