If you want to make a succesful case against another party, then you need to be able to show that they both had a duty of care and were negligent. I doubt there is a strict liability for damage caused by falling trees, that would be a local legal issue but it would be very odd for that to be the case.
I do not think the duty of care would be an issue. You mentioned the storm, but lets say there was no storm, the property owner knew in allowing you to park there that the tree was rotten and could reasonably forsee the incident - then you have a case.
As @Cynthia-and-Chris1 said things happen, does not mean somebody else is responsible.
David