|If other peoples Laptop/Games consoles work fine, the router must have an internet connection.|
What do you mean the "gateway address"? Im guessing that you might mean Default Gateway.
You should only need this if the router has had DHCP switched off. And you are having to type in a manual IP address.
On you PC, open "network & sharing center", click manage network connections, right click your wireless network adaptor, select properties, Double click Internet protocal Version 4, change settings to obtain IP address automatically, and to obtain DNS server automatically. Click ok two or three times to exit out.
The network adaptor will now try to collect all the needed info from the router.
Try the internet now.
Additionally, Have you tried with an ethernet cable? (this will rule out an incorrect WEP/WPA key being keyed in)
If you still can't connect, please access command prompt and type ipconfig /all and paste the results back here.