I dunno if you've tried this but no one seems to have made mention of it, but have you tried clearing the entire cache and history on IE and FF? I used to work at a call centre for a password protected site which required a certificate to access the encrypted site and one of the most common issues was a simple bad file or too many instances of the same file or cookie in the cache ironically enough.
So try it In IE click tools, internet options, and under the browsing history title click settings, then click view files, press Ctrl + A, and hit delete. Next go back and click on view objects and see if any of the installed objects are broken (there will be text saying the object is broken or not running) if there are any like this select and delete them if not leave them alone. Now close IE and then start a fresh session and see if you can get onto your website.
In FF click tools, options, privacy, and look at the private data heading - click on "clear now" another window will pop up tick everything except passwords (deleting the history will not delete your bookmarks) and clear the private data. The close FF and open a new session and try to access your website.
This is not guaranteed to fix it but it can't hurt!!! Let us know if it helps