What specific browsers work OK on your system? Also, can your Opera browser connect to a non-https site (eg: the map at http://squall.sfsu.edu/gif/jetstream_init_00.gif )? Finally, if it will connect to a non-https site, are there any https websites with which Opera will connect?

The insecure connection warning involves the inability for a browser to obtain the proper and current website security certificate and/or negotiate the correct encryption protocols associated with the certificate in creating an https connection to a website. Internet Explorer, Edge, and chromium-based browsers like Opera and Chrome use the site certificates stored locally (and kept updated) by the computer's operating system. Other browsers (like Firefox) use their own certificate stores obtained (and kept updated) from the browser-maker's servers.

If a specific certificate is outdated or revoked, attempts to use it to set up a link to the related https site will fail. If the certificate store itself is not present or access to it is being blocked for the browser installation, no https sites at all can be accessed. If there is a problem or mismatch of the encryption protocols specified by the certificate and those available on the computer, a specific https connection can not be made. Finally, as @burnout426 notes, if your computer is using a proxy for Internet connections, it may cause problems with certificates and negotiating https communications.