Also check the brake fluid level in the reservoir! It may be low indicating a leak or that the brake pads may be worn. E brake switch may be another cause for the light to stay on but my guess is low fluid or bad reservoir sensor.
The brake cable is probably just sticking a bit due to rust on the cable. Spray some lubricant from one end to the other and work the parking brake till it is smooth and free and see if the light goes out. If not it may need an adjustment.