The brake cable could be bad but your rear brakes might still be OK. (The hand brake only works the rear brakes.) If you have rear drums, the typically self adjust when backing up and applying the brakes. Try stepping on the brake 5-6 times whild backing up to see if this 'adjusts' your rear brakes at all. If that doesn't help, put the rear of the car up on jack stands and turn the rear wheels by hand with the e-brake pulled to see if it is working. You may need to pull the drum and look for brake fluid on the shoes or other problems. Although the front brakes are much more effective at slowing the car, the rear brakes do help out. Yanking up hard on the e-brake should be able to lock up the rear tires.
