by Rick Jerz.
I am not an IT person, but I will offer an idea. Might it be something with your area Internet company? I have had a similar problem once or twice, and found that the problem was with the ISP.
See if you can access the site from https://www.megaproxy.com, which is Megaproxy. If you can, then contact your local ISP. If not, then it could be a problem with your server company.
Just an idea???
You can also try copying your moodle installation to an "experimental" server, even with your same server company, or a different on.
Are you running many add-ins? Maybe the problem has something to do with one of these in 2.6.2.