IF you can get his insurance to pay (you have no police report so thats a big if) and the damage is more than the car is worth then they'll cut you a check for the amount that the car is worth.
I learned the same valuable lesson you did a while back. Some kid on his way to school (high school) hit me on my back door, he ran a red arrow light when I was crossing the intersection. He didn't have his driver license with him so he begged me to go with him to his house so he can get it. I felt bad for him and agreed. His mom asked me if we could settle the damage when her husband got home from work and I agreed to that too. Well his dad insisted it was my fault, and the stupid kid said it was me that ran the red light. By then it was way to late for a police report. I still have the dent on my car
Good luck, I hope you can at least get your car repaired.