RJR, You are hard headed. Your first 2 statements are wrong.
I have fixed hundreds of these boards. What else do you want me to say?
You said Voltage on the charging circuit (what ever that is) I assume you mean 2 pin battery terminal with BCR disconnected would tend to mean a BCR short.
WHY? You didn't state it was good, but you implied it was, because you state it means the BCR is shorted.
Go search on some of my other post where I explain how the power supply works.
The charging circuit is separate from the voltage present at the battery terminal. You need to observe the voltage on the terminal dynamically while under load of a battery or BCR to understand what is going on. 5V unloaded means nothing in troubleshooting.
0 Volts at the terminal means no voltage present, but does not mean charging circuit is failed. Though nothing will charge if 0V present. But if zero voltage present, the PS-2 board will be dead and never start up. So why would anyone assume it must be a bad BCR if a board won't start up.
If 5V is present that does not confirm that the charge circuit will or will not work.
So nothing you stated helps isolate whether the BCR is bad or the Charge circuit is bad if a PS-2 board starts up, but won't play shutdown sounds.
There are failures when even a good fully charged battery won't play shutdown sounds, and it has nothing to do with the charging circuit. It could be the cut of circuit. So it is very possible the BCR is charging fine, but when power is turned off the cut of circuit prevents the BCR from powering the board. G