Sounds like you're using IE credential caching.
On that machine, in IE
Tools/Options
Select the Security Tab, and select "Custom Level" on the appropriate zone.
Scroll down to "User Authentication" and select "Prompt for user name and
password" (Or make sure that "Automatic logon with current user name and
password" is not selected)
And I think that will clear out the cache.
What's interesting, is that you state even after being prompted for
credentials, it fails. But this should clear it, and you can try again on
that machine.