The breaker you replaced is either closed or open (normally closed). If you have continuity through it, it is doing its job. If in doubt about it, simply bypass it with a jumper wire across the terminals until you are sure.
At this point you don't know why the solenoid is not engaging. Need to take more measurements to see if the engagement power is going to the solenoid, if the solenoid engages if power supplied to it, if the batteries are reaching the voltage threshold of the BCC, and so on.
The Intelletec 800 BCC in my coach used to blow out a component on the circuit board if the current flow got too high. It could only handle a limited number of amps and if my battery bank got real low, enough current flowed to burn it out. Happened every couple years. I kept two boards and a technician buddy would solder a new component in one while I used the other. A new board was about $200, and after 4-5 years they were no longer available anyway. The required component was only a couple dollars, but my buddy's skills & labor was priceless!
An alternative to diagnose & repair is to add another charging path. A device such as Xantrex Eco Charge or the Trik-L-Start will provide chassis charging from the house system at a moderate price. Charging house form alternator can be done by adding a parallel path via a battery isolator device, e.g. one something like this one.
https://www.etrailer.com/Battery-Chargers/Deka/DW08770.html
