Internet connection problem

I installed a lan card, zoom usb adsl modem and a linksys wireless router into one computer which can easily access the internet. How can i establish a wireless internet connection for another computer that has a wireless adapter which can detect the linksys router connection but still has no internet access. Should I install another lancard to accomodate both the network and internet slots of the router. Is there any way to so that conflicts with other device be avoided should i install the second lan card.