I have a Wireless 802.11G Linksys Router, but I haven't had this problem. If you are receiving a Net connection from your service provider and the lights on both the modem and router are indicating that (should be the enet light on the router I believe), then it sounds like it may just be a router setting or something that needs switching. See if you can log into the router from your desktop: I believe it's typically
http://192.168.2.1. If you haven't set up a password, it should be 'admin', and then I would look in there and double check the settings; basically, if you encrpyted the network, double check the keys to log in (you'll need the key you set, such as #1 if it's set to that), the wireless settings (should be on b), and things of that nature. Linksys' routers have a somewhat messy interface with lots of options, so go through them and see if you can't spot something out of the ordinary there. If you can't log into the router, there may want to disconnect the power to it for about 30 seconds and then plug it back in to reset it.
Networking isn't my strongest point, but I didn't have any problems setting up Linksys' routers, and I set up the Wireless G one about a week ago, and a wired one about two years ago. Hope any of that helps.