Well, I am not a technician and mess up terms sometimes. The modem is a router indeed, a speedport 502, standard model by Deutsche Telekom. I learned that it has an integrated firewall, but 1.) the documentation does not mention how to access and set it, by default it should be on (their word in God's ear), and 2.) hardware firewalls of this kind are not comparison with software firewalls: they use to block incoming traffic, but allow too much outgoing traffic from applications demanding access to the internet.
Compare this: with Zonealarm my system passes all tests of Shields Up! with flying colours and is completely stealthy, with the windows firewall or the router firewall alone, several ports are left not only present (answering to pings), but are left open.
I have a look at what has been recommended by you guys. Thanks to everybody!
