Router Modem conflict
 

I have one machine with 2 network card. One card is connected to
highspeed modem and the other to a router, connected to 2 other computers.

When the router is connected, I cannot go on line. When the router is
disconnected( remove cable), I can go online.

Obviously there is a conflict. Can it be resolved ?

I only need a network printer shared by these 3 machines