Have you tried to clean them? Probably just years and years of dust and dirt built up. The ones on my car were pretty grimey when I got it and hung up to. I had a cable lubing tool from my motorcycle days and used that to flush out and lube up the cables. Not a problem since.
My 64 dart had locked brakes too, I just cut the cables out of the rear drums, hindsight is 20/20 if I just soaked them in a penetrating oil, they eventually would have freed up, and I wouldnt be needing to find a new cable now.