Thank you for the answer...
In the meantime,...what I did, I've installed Debian 3.1 "sarge"...with the help of the Debian Bible. Anyway, somehow the problem with the internet connection is not fully sorted.At the start of the installation, when the installer tried to configure dhcp (it is enabled on the router) it failed.'Till now, I was connected on the eth1, and couldn't access the internet at all even if I think I have put the right settings. I've changed the connection in the eth0, and somehow the internet is working...only with konqueror, and kopete. Communication between the router and computer is all right, I can ping the router from the console, and also connect to the router interface with the browser (konqueror and firefox). I can ping from the console any webpage (tried yahoo and google) but wouldn't connect with the apt-get update command (so I can update my the debian system from the source.
I will try to work to see where the actual problem is.