George,
Neither slide should operate if the ignition key is on. The living room slide is run be a hydraulic pump and the bedroom slide by an electric motor. Since the bedroom slide runs when hooked to shore power, you know the motor and circuitry is good. It should also operate when the generator is running. Since the slide motor is a 12 volt motor, it would make me suspect that your house batteries aren't charged enough to supply the needed current to operate the slide motor. When you have an AC source (geni or shore pwr) the battery charger is supplying enough current to run the motor.
Stever