I had already toggled AirPort off/on, unplugged (the only way to "turn off
"), even hard-reset (which didn't take
), my Base Station, and restarted my deuced Mac(hina), but with no joy.
So, at that point I booted into Apple Hardware Test, and after short test came back negative I started an extended test, decided that it was pointless, and shut down
with the power button rather than wait for it to stop on its own, and it was only when I started up again that things righted themselves.
It was definitely the shut-down
that turned the trick.
Edit: I forgot to mention that I was experiencing wildly different issues with two different Base stations.