If both systems are connected through the switch, then both systems should be
able to simultaneously access the net. That is what a switch is for! You need
not make the packets pass from one system to the other. Maybe your DNS is not
properly configured. Can you ping remote IP addresses from
As far as I understand you (it is not that clear), the Trisquel system has
two network interfaces. An Ethernet interface and a Wifi interface I guess
(all laptops and some desktops have that). You can connect the Trisquel
system with the Ethernet cable and then the other system (have you trie