Had problem - tried fixes - now sharing the one that worked.
The problem:
Computer upgraded from Windows 8.1 to the new Windows 10. Then Outlook 2010 email system would not send emails. Variety of error messages about network connection errors but checking other internet use - all OK.
Did searches. Tried a variety of suggested fixes. Sharing the one that worked.
http://www.ajpcsolutions.com/outlook-stops-sending-mail-after-windows-10-upgrade-fix/
In brief:
Run the command prompt as an administrator.
Run this command:
sfc /scannow
Thank-you "AJPC"!