This all depends on where the internet connection enters the network.
If the conncetion comes into the router, all you have to do is configure the primary DNS and gateway IP addresses to that of your router
(start>control pannel>network & internet connections>network connections; then right click on the network adaptor, goto properties, and scroll on the list for "TCP/IP...")
Then the browser should be able to pick up
N.B. it might be worth disabling any firewalls whilst trying to do this. Also, if the browser doesn't work the first time, try removing any internet connections in control panel (and possibly tell your browser to recieve the internet connection through the LAN)
The only other option is to connect an external modem to the wireless PC... but you say thats not possible
This is all I can tell you without more details of your setup...
But, by the sounds of things, I recomend you purchase a broardband router... makes everything sooooo much easier