Have you actually been into the router config to set up the wireless connection parameters and done the same with the wireless adapter card?
On the Linksys the config page is found by entering
http://192.168.1.1/ in your browser.
Choose a unique SSID
Choose a channel (best not use the default channel 11)
Set Encryption on, i.e. WPA-PSK/TKIP mode, and choose a passkey
Ignore everything else for the time being & save those settings.
For the PCs wireless card, open up its wireless utility and input the same info as above (also you should choose "infrastructure mode" not "ad-hoc mode") save save as the default wireless connection.
In your control panel/network settings, look at the properties for the "TCP>your wireless adapter". In the IP address TAB Make sure "obtain IP automatically" is checked.
Reboot.
If all is working now, you can then further improve security by going into the linksys router config again and diabling SSID broacast and you can use the MAC address filter to only allow MAC addresses of wireless network adapters that you want to allow. The MAC address can be found either on a label on the adapter card or by using "ipconfig/all" at the command prompt (windows xp start/run, "CMD") or in Windows98/ME use "winipcfg" in the Start menu/run box and look for the correct adapter's MAC ("adapter address").