Thanks for your replies. It makes me feel better to hear that those of you who were unfortunately involved in these kinds of accidents ultimately had it resolved. I'm sorry to hear that so many of you have had this happen to you, though!

Since my car was old, we had only liability insurance on it, so of course my insurance is not going to pay for any damage on my car...so I just hope that the other company is not too shady and the other driver doesn't lie about what happened. (His insurance company, a major company, said they "Don't base liability on who the police find at fault"- seems kind of weird to me). I would really like this all worked out soon so I never have to think about it again, but I know it will take some time.