You appear not to have the hardware set up correctly. As you have a separate modem and router, presumably you have Cable broadband (NTL or Telewest)?
That being the case, the modem connects directly to the router's ethernet WAN port and both of the computers connect directly to the router, either by ethernet cable to one of its LAN ports or wirelessly. The *router*, and not one of the PCs, establishes the internet connection with the ISP.
At the moment, it appears the router is being used simply as a "Wireless Access Point" to let you connect to the desktop PC wirelessly from the laptop and presumably you have Internet Connection Sharing enabled on the PC's modem connection? However, a router has a DHCP server to allocate IP addresses to computers, so the laptop may have an address in a different subnet from the desktop and they won't communicate. The Router will "route" the internet traffic to/from the laptop, but File & Printer Sharing won't work.