Okay, this is getting weirder and weirder. I finally got to the bottom of this when I inserted a 5 GHZ capable dongle I had tried befoe into one of the Optiplexes upstairs, and it connected with my 5 GHg network with no problem at all. This was in the same room as the router.
So I brought that computer downstairs and connected it to the TV. I was giddy with anticipation. I paired it with the Bluetooth keyboard and mouse, and tried to connect to the same router it had been connected to upstairs, but the 5 GHz network couldn't be found.
I've always known that a 5 GHz connection doesn't have the range of a 2.4 GHz one, but I've never had any reason to suspect that that might be the problem. In total, there are 5 computers here in the living room that all connect without a problem to the 5 GHz network upstairs. It's only the Optiplex with the dongle that does not. At least, I've finally identified the real root cause.
So, now I figured I'm back to where was before -- trying to get that Inspiron to install Windows and use its wi-fi radio. But wait. It gets even better!
I also found upstairs a bus-type wi-fi card (with two antennas) that I'd totally forgotten about until now. It had a tall mounting bracket installed on it, but I also found the box with the short version, and installed that. I even remembered how to get the Optiplex open, and both bus slots were empty. (I only needed the little one.) Now I'm just waiting for my wife's movie to end, and I'll swap the computers out one last time. I'm confident that this adapter is going to solve the problem. The Inspiron will be perfectly fine upstairs as a torrent server.