Departments don't show up in the new ticket form. Help topics do. In order to use the new department, you'll need to map an existing help topic to it, or create a new one for it.
CAPTCHA doesn't show up if you're logged in (on the client side). If you're not and it's still not showing up, you probably don't have GD support. If you're on a shared host, just contact them and ask them if it's supported, because you won't be able to install it yourself (most likely). If not and you're managing yoru own server: http://us3.php.net/manual/en/book.image.php(http://us3.php.net/manual/en/book.image.php)