The trigger in the code:
if ("" == "") {
is from "before page load", so the screen shot doesn't match the code you sent previously.
Can I get FTP access to your server and a url to the page to test with? Please attach the .php page you are working on when posting so I can look at the code to see what might be causing issues.
The notice is causing the warning. It looks like the authentication.php file needs to be updated to fix the notice, but for now you can add this line to the top of the page:
<?php
// Report all errors except E_NOTICE
error_reporting(E_ALL & ~E_NOTICE);
?>
I'll get it corrected in the next build, but that line will make it ignore the notice since it is inconsequential as long as it isn't written to the page.