It would help to know the exact K-Line models. However, your issue sounds indeed like these units have K-Line Cruise and something has gone wrong with the cruise module.
First step would be to verify the integrity of the wiring between the flywheel sensor boad and the cruise module. If that's good, it's likely the cruise board has died, this is a pretty regular occurrence with the K-Line Cruise boards.
The fix is typically to replace them with the ERR Cruise Commander M as K-Line cruise boards are long out of production.