Thanks for posting those pictures FloobyDust!
Tonight, I got as far as testing and replacing the twelve electrolytic capacitors. The only capacitor that was tested having high ESR was C1 (10uf 16v). It looks to be a filter capacitor on the (+) side of the left channel speaker input:

When I was done with that, I did a quick restart on the Variac. The power meter still acts the same. The green LED illuminates but none of the red LED's work when attached to the speaker terminals of my Kenwood receiver.
So tomorrow night I will start with voltage checks and component testing. There aren't too many in this thing

I'll download the spec sheet on those IC's too.
*Well*, I decided to stay up a little later tonight to try to understand the schematics. The green LED (D19) is on the power supply rail to all of the IC's and LED's. When LED D19 is lit, it's telling me that Transistor Q1 is good and power should be at pin 4 of all LB1405 IC's. Pin 3 is where the input from the speaker terminals enter the LB1405 IC's. Do I have this right so far

It seems that if this circuit doesn't function, the problem is most probably the IC's, at least, two of them. I brought this power meter out of its 30 year coma slowly on a Variac initially.
I'll read the LB1405 data sheet.
This is good practice for me. I disconnected the transformer and the two blue output and white center-tap leads test good. The diodes test good. The (+) side of C13 gets continuity to every pin 4 of the four LB1405 IC's too.
*Another update*, I removed Q1 (2SD400E) and it checks good on the bench. I also have continuity from the (+) positive L & R speaker terminals to IC 1 and IC 3. So the problem isn't in that section.
My next plan of attack is to remove one of the IC's and test it on the bench. I do have my Huntron tracker at the disposal too, but I will need some help discerning where that short or problem could be. I'll post the LB1405 data sheet. I also tested most, if not all, of the resistors.
I'll test the to small tantalum caps on the Sencore (C5 & C10) next.
Any hints as to where I should go next? Thank you!