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It really does sound as if www.example.com is not taking you to the same page as an internal link within the site. I can't see why it should create different results in FF and IE but check if you have both an index.htm and an index.html.
Also try entering the full address of the home page in the address bar in IE and see if that gives a different result to just using the URL.
What if you refresh (F5) the home page? Or Ctrl+F5 (force download)?
Hhhhmmm, I'm sure there has been a similar thread on this topic recently, but I can't seem to find it....? (Images in links, files served locally...?)