I've got a similar problem whereby the homepage was giving a 404 error, but /index.php was OK.
I'm using IIS7 and I got around this using a custom 404 that re-directs to index.php
However, I have noticed that once logged in to admin the page shown is /wp-admin/Index.php although I cannot find any instances of a capital I anywhere.
It seems that this capital I is causing the headache with the homepage not working.