Here's the solution to my problem, thanks to Apple Support. It was not Catalina. It was Malware installed probably through a Flash update in October. First, download Malwarebyte. It's free and it will find malware on your mac and delete the files. There was one file it could not delete so the Apple Support guy had me physically delete it.
I first noticed the problem when Google Earth Pro could not connect to server and would not boot. Then I had intermittent problems accessing the internet and using email.
What the malware did was to check a setting in Proxies in the Network Preference pane. None of those boxes should be checked. What this did was essentially hijack any use of the internet, even though the Network pane said that the Ethernet and Wireless connections were fine.
To fix that get into the Network Preference pane (in System Preferences). Click Advanced. Then choose Proxies. None of those "protocol" buttons should be checked. The malware kept on rechecking "SOCKS Proxy". Unchecking it works, but if you don't delete the Malware file when you restart your machine it will be checked again.
Anyway, everything is fine now for me.