If a hit and run vehicle knocks an insured moving vehicle into your liability-only parked vehicle whose insurance pays for damage to your car?

The "At Fault" party is responsible for your damage, regardless of who ran. The driver who ran from the scene is not necessarily the at fault party. The question is who caused the accident? That person is responsible for the damage.

=== === == It seems that you alone will have to pursue payment from the insured vehicle that hit you. If you had comprehensive coverage, your insurance company would have paid for your damages (or totaled your car, whichever is more prudent) and would have gone after the insured vehicle that hit you. As it stands now, you can try and work with the insurance company of the car that hit you or sue the driver for repair costs. Both are laborious processes. Do yourself a favor and buy comprehensive insurance, which isn't too expensive and, trust me, will come in handy one day.