I'm still not 100% convinced you have a BIRD, but since you can hear the solenoid click, it's pretty easy to figure it out and troubleshoot the system. If neither of your batteries are heavily discharged, this is how it should work:
1. Apply shore power and turn coach battery switch on. The solenoid should click in about 30 to 60 seconds.
2. Verify again that the voltage on both sides of the solenoid is the same. Then check the engine battery voltage, which should within a tenth or two of the voltage at the solenoid (definitely over 13 volts). If the voltage at the engine battery is lower than at the solenoid, suspect the big fuse has blown.
2. Disconnect shore power. Wait for solenoid to disengage (on mine, turning off the coach battery switch forces this, otherwise it can take up to an hour). Start the engine. The solenoid should click in about 30 to 60 seconds.
