Car accident with a rental

What does your own insurance company say? It's possible that they will subrogate and handle this matter on their own. They would pay for the attorney, you would get (it depends on the state, but a lot of them are like this) a percentage of the damages based upon fault, minus your deductible. Since your car was parked, you're either 0% at fault or very near that.

If your own insurance company will not give you satisfaction, you can to your local bar association or call them and ask for a referral to an attorney who will handle plaintiffs' insurance matters (automotive). Since the driver was not the person on the rental agreement, it is entirely possible that the driver was not insured so you would need to make a claim versus the rental company, possibly also the person the car was rented to and maybe also a state uninsured/underinsured motorist fund (cannot recall if NH has that, New Jersey does or at least used to so it's a possiblity).

In any event, most attorneys will handle a case like this on a contingency fee basis. That means that you would pay them 1/3 (sometimes it's 1/4, but this is just a property damage claim, so it's more likely to be 1/3) of whatever the settlement amount is, plus court costs. The bill would be due after settlement or verdict, although you might see bills for court costs throughout the course of the case.

Retain a lawyer. This might be complicated and just a letter, while it may get you some $$, will probably not get you as much as you could by retaining a lawyer and having him or her advocating for you all the way. Keep in mind that the other side, e. g. the rental company, their insurance company, and the renter and the driver, all want to get away with paying you the smallest amount of money it takes to get you to go away. Having your own attorney means that there is someone who wants you to have more than just the barest minimum. Best of luck to you.

It makes no difference if the car was rented and the person driving was not on the rental agreement. Your agreement is with your insurance company, that is why you pay them money. They don't have a choice not to look into this matter totally, they have to look after this matter themselves. How they deal with the rental company and their rent outs is their business. You should not be suing anybody unless your own insurance company refuses to take care of the situation, in which case you should sue your own company only, for just taking the insurance money but not looking after your interests in return. You did your part, now it's your insurance company's turn to do their part.

P.S. If your amplifier/cd player is not something attached to the car then you might have to look into home insurance for that I think.