99 times out of a 100, this is going to be because the ip address of your computer is not on the subnet that your linksys router uses for the internet gateway. If the linksys is configured in the standard way, the gateway address is 192.168.1.1/24. So your computer needs to have an ip address on this subnet, or it will not see the router. I simple test to see if this is the problem: go into a terminal window and ping 192.168.1.1. If there is no response, that's the problem.
Or, in a terminal window, run "ifconfig" to see what the ip address of your nic is. (Ok, I see you have two NIC's now. We need to know the ip addresses assigned to them. ifconfig will report that for both of them.)
If you did not manually configure network settings during installation, RH9 will be set up to get an ip address dynamically. This requires a DHCP server. Your linksys can be a DHCP server, and may well be set up that way. But if both of these are true, then you should not be having any trouble.
IAC, the first order of business is to determine whether the ip addresses of your NIC(s) are on the same subnet as your router.