Eureka. I decided to go checking each jack for shorts.
My prime suspect was the unused jack by the counter where the kids
have breakfast.

My 2-year-old must have jammed something in the jack, because when I
removed it, I immediately noticed that the 4 contects inside the jack
were all mashed together.

I disconnected it, taped up the wires, and everything works.

I got lucky on choosing that jack first!