Without a picture I can't imagine what you're up against. Sound's like you're up sch_tt's creek. The "cable system" is likely the problem. You need to figure out a way to verify the dump valve's gate is opening if at all. It doesn't sound like it is from what you're saying. Can you remove the cable system from the top of the dump valve and operate it manually? The valve stem may be screwed into the gate and somehow come detached either because it broke or unscrewed. I can't believe the tank wouldn't drain once the gate is opened.
Unless it's like mine when I had to take the valve apart to retrieve the disk that was cut out during installation for the toilet connection. Thank goodness enough waste bypassed it I could flush the tank real good before taking the valve apart.
