I did search through the Microsoft Support Forums, and it appears that this is a wide-spread issue.
I suspect it has to do with specific computer H/W in addition to the version of Windows 10.
Quite a few users have tried the methods outlined in the link with results similar to mine. What confuses me is that my laptop definitely "sees" my Roku 4, and recognizes it as an available wireless display, but the Roku never acknowledges the request to connect to it. The only anti-virus S/W that I have enabled is the Windows Defender, internal to Windows 10.
I'll keep experimenting with versions settings to see if I can get it to work.
Please let me know if you come across any additional information regarding Windows 10 and screen mirroring.
"Linoze" wrote: ANOTHER LAZY MAN'S SOLUTION (You don't have to get up and unplug the Roku): -On Roku with your remote, go to settings/system/screen mirroring -Disable it, then -re-enable it -try casting again from laptop or tablet
Truly thought this was hopeless, but FINALLY got this to work thanks to @sharon Hogue's advice: (1) Set Roku screen mirroring to "prompt first" (NOT always); (2) RE-BOOT ROKU; (3) Go to PC action center and click connect; (4) NOW your PC will list your Roku device, but it still won't connect until you; (5) Go back to Roku settings and change to "Always."