It turns out the hinge cables weren't the problem. I bought them before verifying, largely because I didn't want to waste the effort of dismounting and disassembling the dishwasher without having the parts to make the repair. The hook on the spring that one of the cables attaches to was actually broken. I was able to repair it by bending a new hook into the stub left on the spring and re-attaching. Having the cables on hand for future repairs is still beneficial.