Hi - my name is XXXXX XXXXX I'm a litigation attorney. Thanks for your question, but I'm certainly sorry for your predicament.
If your building has rules in place that allows it to tow the car, then it would be virtually impossible to sue because your case would be a complaint that they followed the rules.
Instead, in order to have a case, you would have to prove that they didn't follow the rules and towed your car without providing notice as outlined in the rules, etc. If you don't have something like that, there's probably little chance of success here.
I understand that from a practical standpoint, had someone come to you or even sent a letter asking that the vehicle be repaired or moved, you would have done that at a cost much less than the $1100 that you're now out to move the car. However, the building isn't required to do this - - although the moral thing to do - - if the rules don't require it.
The only thing that could be possible is if there were other vehicles owned by other residents that weren't towed or who were given a personal or written warning before the vehicle was towed. IF that has occurred in the past, then you could sue and claim that the building is selectively enforcing the rules and that you have been singled out. If that is the case, and if you can prove it, then that would be an available claim. Otherwise, I don't see anything there.
I'm sorry my news isn't better, but I'm trying to be totally honest about the situation.