I had someone reverse into my car. I only had third party insurance. THEY should make a claim, and give you the claim number. Then you can ring up their insurance company, state the claim number, and then discuss options to get your car fixed. That's what I had to do. You shouldn't have to make the claim if you're not at fault. But if they aren't willing to make a claim, or didn't have insurance, then I think you're stuffed. Get quotes and find out how much it'll cost you, and see if they are willing to pay for the damage... But yeah, good luck dude. Life's a bitch.