Yes, you may be able to get the pickup truck's insurance to cover your damages. It will depend upon their investigation of the accident and your state's negligence laws.

Even though your vehicle was in a no parking area the truck driver should have used "ordinary care" and proper lookout to see the vehicle there and not strike it. So the other person may be found totally at fault or partly at fault. If it is the latter then likely you will be found partly at fault for being parked illegally.

To find out for certain if the other party's insurance company will pay for all of your damages sustained from this accident place a claim with them and let them investigate the accident.