Well, there are no sales staff, so noone will get those emails. But the others should be OK.
Now that I think about it, someone else had issues with HostGator... but I think they had problems with STMP server...
Can you create a new file with this in it:
<?php
$to = 'support@thewebtrainer.com';
$headers = 'MIME-Version: 1.0' . "\r\n";
$headers .= 'Content-type: text/html; charset=iso-8859-1' . "\r\n";
$headers .= 'From: Email Test <support@thewebtrainer.com'>' . "\r\n";
$body = 'This is a test to check the PHP email function is working OK';
send($to, $headers, $body);
?>
Let me know if what happens. It may be that HostGator is blocking or has disabled this function, although it seems that you are getting some emails to go out! Might sound like a silly question, but can you get emails from other places at this address? Have you checked spam box?