Help--can connect through cable modem but not through router

OK, I need massive help.

I have two computers. I have a cable connection to the internet. Both computers work great on their own connecting directly to the net via the cable modem.

However, once I try and put a router in between them so both computers can use the net at the same time, while one still works, another just simply cannot connect to the internet.

On the problematic computer, I've tried changing out network cards (I bought a new Linksys network card to try and match the Linksys router I was using on the theory that there might have previously been compatabaility issues), I've made sure TCP/IP is installed, I've compared the network card's setting to those of the computer that works and they seem equivalent, I've tried two different routers.

I need help mates. Why won't a computer that can connect directly to the net via a cable modem not connect through a router, while what is a seemingly identical computer configuration on another computer works fine either way?

Please help. Thanks