IT IS WORKING!! HORRAY!!
What made the difference?
For one part the crossover cable, and for the other, that the THICK black cable is the negative pole.
I was fooled by the attached drawing out of the
B&G manual. There it appears that the thin wire is negative.
The shield wire is drawn bigger.
But, it turns out that this thin black wire is shield.
My boyfriend said it's odd that the negative would be thinner than the red positive.
We swapped it and, all is good.
So so happy!!!!