Coverage & Claims
If you can't come to an agreement, or if the other driver won't return your calls, the only other alternative would be to report the incident to your insurance company and let them deal with the other party. Sometimes filing a claim is unavoidable due to the other party not being cooperative in your attempt to pay for the damage out of pocket.
As long as you aren't driving the vehicle and it isn't registered then there should be no issue leaving the vehicle off of your policy. If you plan to drive the vehicle on a public roadway, you will need to insure it.