Hello! While not new to WP, I just started a new job as site dev for a local college (5 days ago). I mention this to frame the situation that I do not have an intimate knowledge of the code yet.
I have never seen anything quite like this though. The site is on WP 3.3.1 using a custom theme. When I go to the themes 'options' page under appearance -> theme options, a number of strange things happen.
* The top admin bar is gone
* The sidebar will not collapse to icons/ expand from icons
* The sidebar flyouts do not fly out on hover
* The footer (Thank you for creating with WordPress) is gone
* The 'Screen Options' pulldown is missing
These things only happen when in the custom themes 'Theme Options' page though. Every other admin page works fine.
One more thing to note is that when I try to add or edit a post, the WP footer (thank you for creating w/ wp) is floating in the middle of the screen. But that is not a priority (yet :)