A firewall normally would block the whole site not part of it (such as a banner). Firewalls operate with ports and IP address and the port and ip address that the site uses will be the same as the banner. The only exception I can think of would be if the banner is a direct linked image. It would give a 404 page not found message where the banner should be. What is the site(s) you having issues with and does it give an error message (or the typical broken image icon)?