You shouldn't leave the car-park without at least an incident report or affidavit. You can legally claim that they're liable, as the non-liability clause on the parking ticket constitutes an unsigned contract... in other words, you don't sign on the parking ticket, you don't necessarily agree to the conditions... and according to Philippine law, you cannot sign away your rights anyway.

For example, even if you sign a contract with a guy permitting him to kill you, he can still be charged with murder... :lol:

Unfortunately, since you've left the premises without such, your best bet is to go through insurance instead. I doubt the management will accept your claim without a report, and so long after the incident. It's worth a shot, but it's dubious.