How do you open the hood of a 1991 Chevy Corsica when the hood latch cable breaks off in your hand?

If the cable itself is still there get a pair of Vise Grip pliers and you should be able to pull it. If the cable is broken up inside the housing then you will need to remove the grill insert. I have a 92 Corsica and there were 4 screws that held this item in place. Reach up and move the lever that the small cable is attached and the hood should pop up as normal.