Can a cpsess unique token requirement cause problems with wifi system?

I've used cPanel for years as webmaster for a small non-profit. Lately, however, I started having problems with the cpsess token. At first, accessing cPanel required several repeat entries of username and pw to get in. Then, late last week, things got progressively worse until nothing at all would work - not only was I locked out ("Page not found") of cPanel (mywebsite.org:2082) but also the website itself, and even the website of our web hosting company! This Page Not Found problem extends to three computers in my apartment, plus two unrelated computers elsewhere connected to the building's wifi system. My contact with the web hosting company asked me whether I had somehow deleted the site's index file. I told him I had not done anything beyond trying to access the cPanel page. The st range thing is that friends in other parts of the city have reported no problems logging into to all three sites. I am very puzzled.