Looks like you need to find the setting in your host’s control panel to make “index.php” the default instead of index.html. Failing that, you may be able to use .htaccess to do it but thats not nearly as good. Check in the host. Stick up any old HTML page, call it “index.html” and see if it shows. If so, then thats what you need to do.
EDIT: Second thoughts, it doesn’t look like PHP is installed. You can view non-PHP files but get a 404 on php ones.