1992 Ford Fairlane Handbrake appears jammed

You can try lubing the cable as it's probably frozen in position. It may break loose. If not you 'll have to take the cable off, soak it in fuel oil for a few days, free it up and then reinstall it. It's the one that runs to the rear axle, not fun to take off but doable if you have time. By the way it's a Parking brake not an emergency brake.