A well thought out discussion. Thank you. As you mentioned, further information is probably needed.
There was no dog serch or anything he just looked through the cars.
That fact pushes your circumstance further away from the fact patterns where warrantless searches have been allowed.
What happened that provoked the searches? Was there a report of a suspicious vehicle? A report of drugs or paraphernalia?
There was nothing at all he went through it for no reason.
He found nothing. He took nothing. He damaged nothing.
Still, in these circumstances it strikes at the interests protected by the Fourth Amendment and has the odor of unreasonableness. At a minimum follow Attorney Jones' suggestion and file a complaint with the school. If an attorney would provide you with a free consultation, it might be worth looking at doing so.
Great answer by Mr. Henderson--but the school cop did not go through your car for no reason. He just did not want to or could not tell you the reason. It may have implicated the privacy rights of another student.