Have you contacted the driver’s insurance company yet? If not, I would start there. You may also want to contact the police and file a property damage report. If not, you should look into this because your insurance company may require a report before paying out on your property damage claim.
If your insurance company does not require any reports, then you could always make a claim with them and let the other person deal with your insurance company when they want repayment from him.
The answer to your question is that yes, the person who backed out of their driveway and struck your parked car is liable to pay the damages. Simple.
This answer is offered for informational purposes only. It is not offered as, and does not constitute, legal advice. Laws vary widely from state to state. You should rely only on the advice given to you during a personal consultation by a local attorney who is thoroughly familiar with state laws and the area of practice in which your concern lies.
The answers above have done a good job of discussing some of the issues that you might encounter. The one thing that I wanted to add is that you should document the damage done to your vehicle -- get an estimate and take photos. These often prove invaluable.
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