Well, it apparently wasn't a hardware problem. But apparently it wasn't a software problem either.

I took the computer to the computer store, and once there it magically began working properly on all eight USB ports without them doing anything other than plugging it in and testing each port with a USB mouse. Exactly what I had been doing, except for me four of the ports wouldn't work. Now they do.

I was not imagining this problem. The problem came on over a period of a few hours, the first sign was when one of my external hard drives started getting flaky, with the computer "seeing" it less and less often, finally nothing would bring it on line, except for plugging it into one of the USB-2 ports. Then it worked fine. Then other peripherals started failing (the USB-3 ports were feeding a pair of 7-port hubs) until nothing worked from the backplane except the USB-2 ports.

The computer shop wouldn't take any money for "fixing" my problem.

tanstaafl.