I think it’s the base_dir path being prepended to the image path - not the other way round.
Now, I had a look and also get the error but on the mysql.png image - looking at the image link, it’s different to the other image links in that it’s referencing the image as a full path (rather than relatively):
http://70.32.93.98/assets/templates/blackgold/images/mysql.png
I’d put money on the fact that IE is passing the link URL back differently to the other browsers and that is triggering the base_dir error. You have a <base> tag so you should be fine keeping all links etc. as being relative paths.
Try changing that link to be relative (and repeat if it trips on other images) - see if that works. Curiously, do you have safe mode/open_basedir settings activated in your php.ini? It may be worth looking into disabling them if you have further problems (or if not in php.ini, there’s a remote chance that the host is setting them elsewhere)
EDIT: One more thing, check your plugins - looking at the location of the error in the document parser class it looks like the file_exists() call is originating from a plugin. Do you have a plugin that is perhaps checking images links? (quick way to find out the culprit plugin is to disable them one by one)