Unless you have seen the person hit your car, there isn't much you can do about it unfortunately. It's best to just get the damage repaired at your own cost. File a police report and take pictures of the damage. Get information from the driver who hit you and from any witnesses. If you skip any of these steps, collecting insurance could be more difficult. Even if the other driver is gone, you could be blamed for causing the crash and leaving the scene, as part of a fraud scheme (they return after they see you leave, and they call the police). Your word against theirs, and you're the one who gets arrested.
Generally speaking, the driver in motion is considered to be at fault when a parked car is hit, even if the car was parked illegally. The exception to this would be if the car was parked in a dangerous, hard-to-see location and the driver in motion could not have reasonably avoided hitting it. For example, if a car is parked on a sharp curve in the travel lane of a narrow road, and the driver of a car driving around the curve at the speed limit would not be able to see the parked car until too close to it to avoid a collision, then the driver might not be liable for damage to the parked car, and indeed the driver who parked the car might be liable for damage to the car that hit it.
Of course it is your fault. The fact that the car was illegally parked is of no consequence. You didn't look where you were backing or you would not have hit the parked car. Would you have hit this car if you had been looking? Perhaps the illegally parked car is a Mini Cooper, parked illegally 1 foot behind a Hummer and therefore not visable when the driver looks before backing up...
You hit a parked vehicle. No matter how or where it was parked, you are responsible for the damages. If you hit the car, you could have seen the car if you had been looking. You have no insurance which is a violation of the law. Pay the owner of the car you hit and accept responsibility for your poor driving, and stop trying to blame this on how the vehicle you hit was parked. It is your fault plain and simple.
Sure you can sue anyone for anything. The question is will you win. Let's get this straight. You hit a parked car, and you want to sue the owner of that car's insurance company. And your reason is that the car was not registered. Well if the car was not registered then how did they have insurance? What does the fact as to weather the car was registered or not have to do with the accident? You hit a parked car and that means you were at fault. But you go right ahead and sue. See where that gets you.
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