Man Backed Into My 20 Year Old Car And His Insurance Won't Cover The Damages, Need Help :(

I had my car parked in front of my house curbside, and the neighbor's yard worker backed into my 20 year old car and caused damage to the back. They gave me their insurance card and everything, their insurance and mine both stated that they were found liable from the accident. He admitted to me in person that he didn't see my car when he backed into it with his work trailer.

If his insurance doesn't pay, what should I do? Would I be able to file a suit in small claims court? Or would I be able to work something out with their insurance to find a repair shop that would repair it in the range? His insurance agency hasn't been of much help on the phone :(