Are you using a DHCP client, or are you using a static address when connected to the linksys router? You should set up the connection as a normal LAN connection.
The linksys router probably has a web based interface. Point your browser to 192.268.1.1 . By defaullt the 'username' is blank and the password is 'admin'. The status page will show you the WAN ip address of the router, and the DNS addresses. There is a 'DHCP Clients' button you can push to get a table of the local LAN clients and their DHCP assigned addresses.
If you are using a static address, make sure that you pick on below the starting DHCP range. ( Below 192,168.1.100 )
Also, copy the DNS information from the status page. With DHCP this information, as well as the gateway address is provided to your computer.
If you change the equipment connected to the cable modem, you will need to register the equipment's MAC address. This is normally done by pointing your browser to the home-page of your ISP.
You might want to provide the output of 'ifconfig'. If you can connect to one of your windows machines from linux, or if you can view the Linksys setup page, then your NIC card is probably set up. Otherwise provide the output of 'lsmod'.
Also, make sure that you don't have a different device on your local network that uses you DHCP assigned IP address.