State laws may vary but in general if you back up or reverse into a vehicle, you are usually found at fault. In some states it is called not having "proper lookout" if you hit a car, even if they are illegally parked, in this manner. If the other party places a claim with your insurance company, then your insurance company should investigate and determine fault and if they will pay out on the claim.
When your insurance carrier's claims adjuster investigates the claim, they should be advised of the previous damage and should take that into account. Your claim should only be paying on the actual damage you caused the vehicle to sustain in your accident.
The value of the other party's vehicle will be taken into account, such as that your insurance company will not pay out a claim for more than the car is worth. If the damages it received in the accident from your car hitting it would cost more than what the vehicle is worth the insurance company would total out the vehicle and pay only the actual cash value (ACV) of the automobile.
You will need to discuss the accident with your insurance agent to find out what next steps to take and if a claim from the other party will affect your insurance rates. Claims against your policy can cause rates to rise but it will ultimately depend upon the rating system of your specific insurance provider if this claim will cause your rates to rise.
If your rates do go up you might decide it is time to comparison shop for auto insurance. You can start here with us by getting a quick car insurance quote.