1978 Rolls Royce Corniche how to open hood with broken latc

If the release handle for the hood doesn't retract back into position after you pull it, it's likely that the cable leading to the latch is broken. If the release handle retracts as usual and you can feel it trying to release the latch, it may be the latch itself that is broken. It is more common for the latch to be broken or jammed than for the cable to be broken.
Rule out the hood being jammed shut before you proceed as if the latch is broken. Have another person stand in front of the car and pull up on the hood while you stay inside the car and pull on the hood release cable. This may help unjam the hood if that is the problem. If this still doesn't help the hood lift up, you can proceed as if the latch unit is broken.
Shine a flashlight through the front grill of the car to locate the latch unit. Once you can see it, use a screwdriver to go through the front grill and manipulate the screwdriver in different ways, trying to open the latch. The latch is spring loaded, so it may take pressure to open the latch manually. Be careful to stay away from the condenser for the air conditioning unit--the screwdriver could puncture a hole in it if you don't keep it only on the latch assembly.