The Netgear WGT624 is a "Cable/DSL" router suitable for use with the NTL or Telewest Cable broadband services - is this what you are using?
The router's WAN port should be connected by ethernet cable to the Cable Modem's ethernet port and the PCs connected to its LAN ports, or connected "wirelessly".
What you say suggests that your computer is still connected directly to a modem, and getting internet access, with the "router" operating as a basic Network Switch and/or Wireless Access Point to connect the computers in the LAN. This won't let the other computers have internet access.
The router should connect to the modem, and thus the ISP, and there should be no *direct* connection between a PC and the modem. All PCs get their internet access over the LAN from the router.