Sounds like a bad spark plug or spark plug wire to me.
As long as the parked vehicle is parked properly and not illegally parked in any manner, then the vehicle that rear-ended the parked car is at fault. Now if the parked car is sitting illegally (such as double parked or parked in a no parking zone, etc.) then the parked car is at fault or even both the parked car AND the car that hits it are BOTH at fault.
Yes, as long as the engine is not in gear and a brake is enabled.A "Parked" car is defined as: a setting in an automatic transmission in which the transmission is in neutral and the brake is engaged. (http:/dictionary.reference.com/browse/park)Therefore it would suffice to say that a car is parked once the wheels are locked via some sort of brake and the engine is not in gear (park or neutral). The lights being on is irrelevant.Concerning California law: It is illegal to leave your vehicle unattended on the highway without first turning off the engine and enabling a brake.(http://www.dmv.ca.gov/pubs/vctop/d11/vc22515.htm)