You're going to have to either pay someone to investigate this for you or start investigating yourself and post back the exact errors you encounter along the way.
I'd suggest a strategy as follows:
1. Enable extended logging in Exim
This, among other things, logs the subject of an email which makes finding a message in the mail logs so so much easier.
http://forums.cpanel.net/showthread.php?t=48648
2. Create a simple PHP script for sending a test message
PHP Code:
<?php
mail('myaddress@example.com', 'my easy-to-spot test subject', 'my unimportant test message');
?>
3. Set the subject value sensibly and execute the script. I'd recommend changing the subject each time before executing so that you can track which test message is which.
4. Wait long enough for something to turn up on the mail logs and then check through /var/log/exim_mainlog for the message sent by the script. Act accordingly on any error messages you find.
It's as easy as that. If you don't understand what an error means, post the full and exact error message here and people may be able to help. But first and foremost you're going to have to put some effort into this.