What os are you using to run the firewall machine?
If it's windows you need to install and configure Internet Connection Sharing. Then...once that is installed and working...you can plug nic #2 into the router. The problem with this setup is that the router you have probably runs it's own DCHP. So what you now have is something like this...
Gateway machine
NIC #1 has incomming cat-5 from the modem...
NIC #2 relays (via ICS) to the router...
ROUTER
IN ... this comes from NIC#2 from the gateway machine
OUTS ... these connect to your other machines....
the problem...
If you are using ICS to relay in the gateway machine...and you go to the router...you need to configure the router to accept DHCP and all your other machines to get ip via DHCP. The problem you may run into is that your router may be failing to get DHCP from the gateway machine and thus, no ip addys down the line. With a setup like you want...you would be much better off with a link and that way you can assign all the downstream machines their own private ip addys. (192.168.0.2, 192.168.0.3, 192.168.0.4) That way the gateway does all the firewall protection and also the NAT stuff and then all the downstream machines run through the link like a "splitter". You don't really need the router since the gateway machine will handle the NAT duties.
If you need help with ICS for windows...use google. I suspect that your problem lies with ICS and/or the DHCP on the router. Both the gateway and the router are trying to do the same duties.
good luck