Got it! I plugged the new slider code in and the universal slider disappeared:
Screenshot of header.php with new slider code: https://drive.google.com/file/d/0B6BDYvRiwPg4WjlWcld1TDVnbUU/
Screenshot of how website displays with new header.php code: https://drive.google.com/file/d/0B6BDYvRiwPg4MV93YURWTGo3bmM/