I had the same problem with Safari (Version 5.0.3 (6533.19.4) using a Mac OSX10.6.5. I could log in to the account area but when I tried to open CPanel I got this message;
Safari can’t open the page “https://propus.lunarpages.com:2083/login” because Safari can’t connect to the server “propus.lunarpages.com”.
I logged in using Firefox 3.6.13, and logged in to my account and clicked the cPanel and it worked.
After that I tried with Safari again and, it had the same problem and message. So it must have something to do with Safari!
I was using Safari 5.0.3 with OS X 10.6.5. Although I don't remember the error message. Nor did I try FireFox

So it could have been issue with Safari/OS X.