Well ...
Fiddler seems to look at HTTP traffic, and I saw nothing untoward there. I figured
something must generating this traffic.
Closed all applications, including Solitaire (

). Still data dribbling in and out. The task manager showed system idle running 98%, cpu around 2 %. Hmmm.
I checked the startup folder. Nothing there but Microsoft Office. I normally delete this entry, because Word (or Excel) is started automatically when I try to open a compatible document, and when I want to use one of the Office programs, I just click on it.
Since it (the shortcut) hadn't been deleted, I deleted it.
And the data leakage stopped.
I don't know why, but apparently when Office is run at startup, no programs come up but the Office executive just keeps exchanging data with ... somebody. It doesn't anymore.
Bottom line - I didn't have to buy a Mac, and (sorry to disappoint all the nervous nellies out there) it wasn't a virus.