It turns out that the magic missing piece was....OpenGL. You have to have openGL turned on to make the thing work. The instructions say that your computer has to have OpenGL, and that it has to be enabled, and the dialog shows when it's NOT enabled, but by the time I got there, I'd forgotten that it was required, and just thought "Oh, that shows me which mode it'll use for rendering" rather than "that's an option which, if I don't opt for it, breaks everything."
You folks have done a great job with this, but I'd like to recommend two possible changes:
(1) If I were writing that dialog, it'd say
 Accelerated Graphics (OpenGL) [must be checked!]
and I might even add a button to the right to pop up the relevant part of the Tools...Display...Advanced menu where the user can actually do the checking.
(2) Also, the sentence at the top of the dialog is
"Cannot switch radar on as it is not connected or off"
which is ambiguous: the "not" may or may not apply to the word "off". I'd rewrite as something like
"Cannot switch radar on as it is either not connected or is not off."
(if that's actually what you mean!)
Thanks again for the work you've done on this, and for the quick response to my clueless question. As a computer scientist, I should know to RTFM.