I don't know about Linksys routers or wireless cards, but I have set up a Belkin network at my ex's house, and I have a D-Link system, running at mine. For both of those brands, the instructions that came with the wireless card specifically said, in nice big letters, "Disable the Windows XP management of your wireless connection." I don't know why it causes such a big problem with those two brands, but in my experience, they were right. Whenever Windows randomly decided to handle my wireless network connection for me, everything stopped working
That said though, routers are like printers, for every one good story you hear about a particular brand, you'll hear a dozen "stay away from Brand X, it blew up my toaster!"
On XP, what worked for me was going to Start, Control Panel, Network Connections. Right click on your Lan connection, and select disabled, like Phantom suggested. Then, double click on the wireless connection. There's an option somewhere like "Disable windows management of wireless networks." The computer I'm on is wired, so I don't have it on my screen, but it looks something like that, and I know it always takes me a while to find it. Make sure it's turned off. Then click OK.
Now, run the program that came with your wireless card. It should already be running in your system tray (by the clock, it might be hidden in XP, so click the arrow and check all the icons.) There should be a pretty hard to miss button somewhere that says something like "Scan for networks." Click that and see what comes up. Hopefully, one of the networks that show up will be your router. If it does, double click on it and you should be all set, unless you've set up encryption, in which case you'll need to enter the key you used when you set up the router. (Not the login password BTW, it should be an option somewhere once you log into the router.)
If your router doesn't come up, then maybe like RevDisk suggested it doesn't enable Wireless by default. Log into the router and make sure.