Victim of hit and run on my parked car? Other party unknown?

My vehicle was parked at a college campus while I was in class, during that time it was hit by someone. I contacted local campus police and they cannot see anyone hit my car on the security camera (the camera is at a strange angle and my car is only visible from about 500 ft. away). I have liability and uninsured motorist coverage in Texas from Allstate. Allstate is saying that they will not cover the damage because I do not have full coverage (my car isn't covered if I hit someone and its my fault) However, they also have no one to go after because the person who hit me is unknown. If the person who hit me is identified, and doesn't have insurance, then I am covered under the uninsured motorist coverage. Is it possible for this to be covered somehow? What are my options? It looks like its about $1200 in damage, and my student budget doesn't really allow for that expense. Any help would be appreciated. Thanks.