I don't recall seeing that block in my '67 but it looks like a buss bar to feed the low voltage systems.
Have you checked the 120 AC breakers at the panel in the "Service Center" at the rear.?
If the 12VDC circiuts all went out at the same time after the failed connection to the shore power I would think the battery would have enough juice for at least a day running lights and the furnace.
Sometimes you can hear the converters hum if they're powered up. If not that's the first place to look. The 12 volt
stuff will work off the converter without a battery.
I'm guessing, and its only a guess because you say the rig's been refurbished, that there is some fuse, breaker or connection you haven't located that could be the cause of you problem.