Alright, I got it working for me in a very, very, VERY simple way. It is not all that secure, but for my means it is okay:
//include the config file from PunBB
include ("forum/config.php");
//Decode the forum cookie.
$decoded_cookie = base64_decode($_COOKIE[$cookie_name]);
$logged_in_info = explode("|",$decoded_cookie);
echo "User ID: ".$logged_in_info[0];
Obviously, if the cookie isn't set, the user isn't logged in. The user's password is also saved within the cookie and can be cross-checked to verify it is not a spoofed cookie for added security, which I may add eventually but for now this is about all the implementation I am looking for. Using the User ID, you can look up the user's information in the database and echo it all out in commenting forms and stuff across the site.
Anyway, there's my basic solution. Very interested in other people's.