Looks like the CSS isn't being loaded properly. Knowing IE and how it's used in institutions, there are two things I suspect here.
It could be a caching issue. Try clearing your IE cache, or using Ctrl+F5 to force reload the page. Your institution probably passes all web traffic through a proxy server, and those cache things too. That could be an issue.
The second thing I suspect is IE's rendering engine. View the page source (try the View menu, I can't remember exactly where IE puts this option because I use a Mac).
What is right at the start of the very first line of your page's source code? It should start <!doctype with nothing before it, not even a blank space. If it doesn't, IE assumes it's an old page that hasn't been written to modern web standards, and displays the page as if it was Internet Explorer 5. This is called Quirks Mode.
If you press F12 to open IE's developer tools, there should be two options that let you see how your page looks in different IE versions. One of these should say (Page Default) next to it. What does that say? If it's Quirks Mode, your page is displaying in Internet Explorer 5 mode.
If it says Internet Explorer 7 (which could also mangle Moodle's homepage), you probably want to try this. Internet Explorer 8 and 9 have a bizarre feature that automatically detects if a website is running on an internal IP address, and displays the page as if it's IE7.
