MS stupidity...

I finally got to the point where I could get Windows Update to at least give me an error code when the attempted updates failed.

But MS had *no* results for that code when I searched for it on their site.

By accident, I entered the code into google. And the very first hit had a solution that worked:

net.exe stop wuauserv

regsvr32 wuapi.dll
regsvr32 wuaueng.dll
regsvr32 wuaueng1.dll
regsvr32 wucltui.dll
regsvr32 wups.dll
regsvr32 wups2.dll
regsvr32 wuweb.dll
regsvr32 MSXML3.dll

net.exe start wuauserv

But rather than type it in one line at a time, I saved it as fix.cmd and ran that.