A couple more ideas.
Do you have access to the server daily log – that's the long detailed one that shows every browser request and the server response? There might be some more information in there for the time the error occurred.
What are the permissions on the index.php file in the root?
Backup your index.php file, create a new index.php in a text editor with the following content and upload it to the root
<?php
print "Hello World";
If that one gives a 500 error then it's definitely something to do with the server and you should take it up with your server admin or helpdesk.
If it displays 'Hello World' in the browser then is there any difference in the permissions on this new index.php file and the old one that didn't work? Some servers will not run a php file if they think the permissions are not restricted enough to be secure.
jack