Windows cannot update

Sat Aug 3 16:28:00 GMT 2019

I'm reaching out in desperation to a knowledgeable group. The difficulty is not Cygwin related.
I am using Windows 7 Pro 32-bit. (Yes I know, but with 6 months to go it's not completely daft.)
For 10 days I have been unable to update , getting a "Windows could not search for new updates" error message with a 8007000E error code.
I've been online and tried EVERYTHING from sfc to renaming WINDOWS\SoftwareDistribution and off-ing and on-ing key services to installing the Update application (didn't know there was one, additional to "Control Panel > Windows Update") to endlessly reconfiguring the Windows Update settings. I've even re-installed from a Windows 7 Pro SP1 iso, but landed in the same place. Windows is activated just fine, it just refuses to Update. 
I've had it before and have some kind of recall that it fixed itself when I wasn't looking or trying. No such luck currently.
As stated above, I have other machines with perfectly configured and maintained Windows 7 Pro 64-bit, and Windows 10 Pro. But I just want this one to work too. Have any of you accomplished savvy tekky people been here yourself? Do you know EXACTLY what to do? 
THANK YOU for bothering to read this.

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