I think I saw your error:
if the query is returning and doing nothing is because the condition is Wrong. If you try the query in PHPMyAdmin the Query is OK, the only thing I can think is in this part:
$msgID = $POST['message_id'];
$msgTitle = $POST['message_title'];
it should be:
$msgID = $_POST['message_id'];
$msgTitle = $_POST['message_title'];
if it doesn't work make:
print_r("DELETE FROM messages WHERE message_title = '$msgTitle' AND message_id = '$msgID'");
and let us know the output