Man - what a pain in the ass.
Apparently the in built CodeIgniter session class and IE don't like each other.
On top of that, if you're using an internal computer name to access the site, well, that's not a valid W3C URL standard. You have to have at least two "." 's in the URL. So, trying to access the site via
http://mycomputer is not strictly valid. Sigh.
So, I found the session hybrid class for CodeIgniter. Combining this with accessing the site via
http://www.mypcname.com seems to work in IE. Firefox doesn't give a shit. You also have to put the
www.mypcname.com in your /etc/hosts file to make it work (otherwise it obviously will not resolve through normal DNS).
So, the long and the short is - I have it fixed, but to work in IE will require a change to your /etc/hosts file (or your internal DNS).
This does not affect submitting audit results, as that page does not use cookies.