It seems that your router is not routing anything but rather is just a hub and the modem connects to the first computer it sees, leaving the other one with no connection.
We share our NTL connection around our house to about 6 computers, the trick is our firewall.
We have an old computer running Smoothwall (
Welcome! - SmoothWall). Smoothwall is a dedicated firewall OS built on Linux. Our computer has two network cards in it, one connected to the modem, the red interface and one connected to the LAN, the green interface.
The smoothwall box also acts as a DHCP server which assigns every computer it's own IP address, e.g 192.168.0.xxx. The computers then look for an internet gateway, the smoothwall or they're manually told to look for the smoothwall and they all have their own IP address and share the one internet connection.
If you want to to this, basically you need one old pc, old means old, a 486 can be used but I used a Pentium 1 166mhz, you need to have to NICs in that computer (NIC = Network Interface Card). Connect the modem to one card, set it as the red interface, connect the LAN to the other card set it as the green interface.
I'm sure your router could be used but we need more information on it first.