My Ford f-350 did the same thing, (before I sold it for a 77 c-10) it was the e-brake. Yours probably has a kink in it or is frozen or rusted somewhere. Replace that cable properly, and do a good brake cleaning and lubricate in the right areas. You should not have any slack, and when set...should spring back nice.
My 86 s-10 also froze up bad when applied, I had to floor it in reverse and pound on the brake pedal just to free it. When I donated the truck they "dragged" it away.