There's not really a "program" that DBR uses to access the internet. They put their website on a server, and you're downloading the server content when you type in the address on the web page.
The board itself is a modified version of phpBB, which is probably the most popular bulletin board software out there. The server itself is probably an Apache server.
If you can view the main site, and not the bulletin board, then I don't think your firewall is the culprit.