The firewall is setup to block off traffic except over a few ports. Ports 80 is the standard port for web browser traffic and hence it works when the firewall is enabled. dc-gui like other p2p clients runs on a much higher, which is getting blocked by the firewall.
you need to specify which port you want dcgui to use in the config for that. then in the firewall config you want to open that port for both TCP and UDP. I think common ports used for DC are 412 and 1412 but I think you can actually use any.