I am recalling as best as I can remember.
I was driving by Hadassah hospital — and as you may know the parking situation is very hard. I happened to have banged I think slightly into a car that was parked in a zone that was designated as a not parking area if I remember correctly — I may have been backing up when this occurred. I did not leave a note as I think I thought I was not responsible because the way the other car was parked by a no parking zone.
Question: based on these facts — was I responsible for hitting that car, and if I was how can I do teshuva if obviously I have no idea who the person was.
How much am i responsible for moneywise: — if it was a small dent but the only way to make it really good is to replace panel and repaint is that what I would have to pay?
This is a somewhat complex question.
Although he was parked illegally, if his parking did not obstruct traffic you will be liable for damages according to Torah law.
However, if his illegal parking did obstruct traffic, and he effectively placed himself at risk by parking there — and you were not negligent in hitting him — you will not be liable for damages.
Concerning the liability for denting a car, see here where we explain that the general obligation is to fix the dent.
If you think that you are liable, the way to go some way towards repairing the damage is to contribute the money to a communal cause. Please see here for a short article on the subject.
Best wishes and apologies for lateness of reply.