This is very strange behavior. My cPanel is looking very distorted when I log in from mydomain.com/cpanel but is fine if logged in through <server ip>/cpanel. When I use Chrome to check for errors I see some CSS and images are getting the 401 error. Below is a screenshot of my cPanel. I called tech support and they weren't able to answer my question and help me fix the situation! Not sure if CloudFlare has anything to do with it, but I did install it three days before this post was up. I went into CloudFlare and make sure cPanel is bypass.
Bump! Will put out bounty soon!