Following these general instructions, I was able to open the hood of a 2012 (gen 3) Prius where the cable case was dislodged from the seat of the latch attachment.
Details: With the car on jack-stands, I removed all under body panels from the front underside of the car. While under the car, using a flashlight from the passenger side with my right hand and looking up from this angle, and a 28" 1/2 PVC pipe going up from behind the radiator on the driver's side using my left hand, I was able to reach the bottom of the latch arm and push it to the passenger side. (The cable pulls the top of the same latch towards the driver's side.) Very little pressure was required to move the latch horizontally about 1/2 inch. This simple action released the main latch which allows the hood to be opened from the top of the car as is normally done. Hope this helps...