Are you using a Linksys WRT310N? Why not simply replace that piece of junk with the Extreme - it's a much better, more capable and more reliable router.
In any event your description confuses me but here is how your equipment should be physically connected, if you have reason for keeping the WRT310N in service as a router:
Next, using AirPort Utility for Windows, select the Extreme, click "Manual Setup" and make your configuration conform to the following settings:
Internet pane > Internet Connection tab > Connect Using > "Ethernet"
Connection Sharing > "Off (Bridge Mode)"
TCP/IP tab > Configure IPv4 > "Using DHCP"
AirPort pane > Wireless tab > Wireless Mode > "Create a wireless network"
Wireless Network Name: make it exactly equal to your existing wireless network name
Wireless Security: make it exactly equal to your existing wireless network security
Channel: leave it on Automatic unless you have reason not to
Update and let the Extreme reboot.