If I had to guess, there's a broken wire in the wiring harness somewhere. I would call Cateye and explain your situation. IME, they have good customer service.
In the meantime, take a look along the harness for any broken wires, damaged insulation, or wires pulled out of their sensors (even a little). This can sometimes happen if a wiring harness is installed or wrapped too tightly. I always leave just a tiny bit of slack at both the computer and sensor ends.
They're probably both still usable- at worst, you're out the cost of a new wiring harness, which Cateye sells on their website.