Well that was not a story with a happy ending. 
Those multiple 5mm exposed slits in the wiring is suspicious suggesting this engine was an accident waiting to happen...and wouldn't you know it, it happened!
If the component you changed was the one above the black wire in your photo, that drives the smoke heater so I would not expect it to have changed anything wrt the battery/BCR operation.
No sound on a PS2-3V is typically a blown audio amp IC on the lower/larger so-called Processor Board which is a tedious soldering job of a $3 chip. The audio IC has been known to blow if you indeed have exposed speaker wiring. There have been many threads on this. Loss of speed control following the fondling of the wiring harnesses could be a loose/shorted strand of wire in the 3-wire blue-gray-orange tach wire set where soldered to the tach board on the motor.
I'm thinking this is a lost-cause... just my opinion of course. After all, something caused the battery/BCR circuit which started this trip down the proverbial rabbit-hole.
Actually, in the lemon-lemonade category I wonder if there is any "scrap value" to a PS2-3V board that exhibits your board's behavior. Since it appears the PS2-3V Processor Board is no longer available, and it does seem to do some things, I wonder if there's some salvage value to the right person.
