I was working in a recently updated image where IE got updated to version 11, I was facing the same problem and the log didn't show any error. In my case it's still ES3 SP2 but indeed, looking at the supported browsers, IE 11 is not even mentioned for ES4.
First, I've noticed that installing Chrome (now at version 33.x) all admin pages got displayed. Second, turning on "Compatibility View" for the LC admin website allowed the page content to be displayed also on IE 11.
When looking at the page source for the blank pages, all they contained was a SAML assertion so there must be an incompatibility between IE 11 and the way authentication/authorization is managed in Adminui.
It would be worth publishing a tech note about this problem, and hopefully a future SP will address this incompatibility. For security reasons, it's nearly always a best practice to keep browsers updated and therefore IE 11 should spread pretty fast.
The answer for now, therefore, is to use Chrome (and possibly also Firefox but I haven't tested it) or to turn on Compatibility View in IE 11 for any address where the Adminui web application is running.
