There is security software like Avast, Kaspersky, BitDefender and ESET that intercept secure connections and send their own certificate.

https://support.mozilla.org/en-US/kb/firefox-cant-load-websites-other-browsers-can

https://support.mozilla.org/en-US/kb/firefox-and-other-browsers-cant-load-websites

https://support.mozilla.org/en-US/kb/secure-connection-failed-error-message

https://support.mozilla.org/en-US/kb/connection-untrusted-error-message

http://kb.mozillazine.org/Error_loading_websites

• uses an invalid security certificate SSL_ERROR_BAD_CERT_DOMAIN
• configured their website improperly

How to troubleshoot the error code "SEC_ERROR_UNKNOWN_ISSUER" on secure websites https://support.mozilla.org/en-US/kb/troubleshoot-SEC_ERROR_UNKNOWN_ISSUER

In case you did use the refresh feature in Firefox you can check the "Old Firefox Data" folder on the desktop and copy cert9.db to the current profile folder with Firefox closed. If you only see cert8.db then copy this file and make sure to remove an existing cert9.db file.

• https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile

You can use the button on the "Help -> Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page.

• Help -> Troubleshooting Information -> Profile Directory:
  Windows: Show Folder; Linux: Open Directory; Mac: Show in Finder
• http://kb.mozillazine.org/Profile_folder_-_Firefox

You can check if there is more detail available about the issuer of the certificate.

• click the "Advanced" button show more detail
• click the blue SEC_ERROR_UNKNOWN_ISSUER message to show the certificate chain
• click "Copy text to clipboard" and paste the base64 certificate chain text in a reply

If clicking the SEC_ERROR_UNKNOWN_ISSUER text doesn't provide the certificate chain then try these steps to inspect the certificate.

• open the Server tab in the Certificate Manager
  • Options/Preferences -> Privacy & Security
    Certificates: View Certificates -> Servers: "Add Exception"
• paste the URL of the website (https://xxx.xxx) in it's Location field.

Let Firefox retrieve the certificate -> "Get Certificate"

• click the "View" button and inspect the certificate

You can see detail like the issuer of the certificate and intermediate certificates in the Details tab.

Thank you so much for taking the trouble to reply. I am keeping your responses in case this happens again. After a morning of fiddling around using other ways of going online and still getting the same 'insecure connection' to Google I gave up and turned off the computer. When I turned it on again the problem had mysteriously resolved itself and connection to Google was back!!.... how did that happen??

Could be a corrupt file was removed. As long as it works.

Please flag your last post as Solved Problem so others will know.

Problem solved.