I have a very similar setup that works like a charm.
Hello.
I use a very similar setup at work and home. Piece of cake to set up.
First, reset your router by holding the reset switch. If you use DSL for highspeed (think you said you did), make sure you have the logon for it (if your DSL requires it).
Next, set everything up like the diagram I attached.
The Linksys router will have the DHCP server enabled by default. This will give out IPs in the range of 192.168.1.100 -> 192.168.1.150. This is fine, you can leave these on. Don't worry about trying to be more secure by using other IPs, you'll just have more problems.
The Linksys router will have an IP address of 192.168.1.1 . This is ok. The default password will be admin. You will want to change this as soon as you log in.
If you hook everything up like in the diagram and have your computers set to automatically obtain an IP, then they should be talking. You should give them both a reboot though just to make sure they grab a new IP.
The first computer to obtain an IP address will be given 192.168.1.100. The second will be 192.168.1.101. Go to a computer and go Start->Run->cmd . At the command prompt, type " ipconfig ". If the ip ends in 100, try to ping 192.168.1.101. If the ip ends in 101 , try to ping 192.168.1.100.
The reason I put the XBox at 192.168.1.151 is because that is outside the IP pool of the LinkSys DHCP server. I have a playstation and give it that address because I then enable the DMZ in the router and point it at that. Makes life easier.
Anyways, this is just the basics... I'm tired and its late.. Tommorrow I will get into securing your wireless and setting up port forwarding and such so that you can use things like BitTorrent at full tilt.
Cheers,
TdeG