Several years ago, I had something similar happen though it was a tad more clear cut.
I was living in an apartment complex with assigned spaces. I came out and saw my rear bumper had been side swiped. I also saw the pos dodge charger with scrapes all over it, but it had one that was perfectly placed and colored to have been what hit my car. Now, I had no proof of this.
As I was out looking at the car, the girl who owned the dodge was coming out to leave. She was clearly severely hungover. She tried to deny it, but luckily the guy she took home at the time was there also and made her fess up to it. Once she admitted it, then she is on the hook now matter what and that's really all you can do here. Try to get them to admit it and get their insurance information; also take pictures of both vehicles damages. Getting the insurance info will be key later in supporting your claim that they admitted fault. This women then denied it to her insurance company and they said they wouldn't pay until she confirmed. I called MY insurance company and explained this to them. They called back in 30 minutes saying her insurance company will be paying for repairs at the shop and parts of my choosing. I think there needs to be threat of lawsuit if they fail to pay and it's hard to deny given the damage to both vehicles and why would she have provided her insurance if she was not involved.
I don't suggest making up stories and being mean about it, but rather try to make them feel guilty. Especially if this is a neighbor who will see you regularly and they will have to live with the shame. If you're mean, they will feel like they are justified to screw you. Start off explaining how much you loved this car and how you spent every penny you saved for many years just to get it and you can't afford to fix it if the person who did it doesn't own up to it with their insurance company. Don't directly accuse them, but do say you noticed they were parked there and had a similar scrape. Let them see how crushed you look at the thought of not being able to repair the damage... let the guilt eat them up until they say... ok, yes it was me and then ask for insurance card asap - snap a photo. If that doesn't work, then by all means lie and intimidate
