Hello,
I faced this problem one one of my MODx websites too.
All the images inserted in the website were broken, as well as all the links in some areas of the website (tag cloud for example).
The problem is apparently caused by IE not interpreting the base href properly.
I changed my base href to <base href="[(site_url)]"><!--[if IE]></base><![endif]--> and placed it at the beginning of the <head> and the problem disappeared.
The weird thing is that this happened only on ONE website out of a dozen I made with MODx. I suspect it is also due to server settings, though I have not figured out which ones.