[alanw]

Clicking at the starter solenoid is usually because of low current at the solenoid. If the battery is good and the solenoid is good then it's a switch going bad somewhere down the line. Check the ignition switch, neutral/park switch, starter relay, or maybe bad wiring somewhere. You can apply power directly from the battery to the solenoid as a test to eliminate both of them as the problem but be careful the car is in park with the e-brakes on or your car might be driving without you