Ok the problem seems to be with the router .
What Security method are you using to connect to the router ?
Please try none for a test , or other such as WEP or WPA2 to connect to the router .
Also please try setting the Wifi channel to 6 or 7 or 8 , higher or lower channels can some times make a router unstable .
Try to pick a channel no one else is using next door , this tool can help find a clear unused channel . .
WiFi Scanner v1.1 http://www.wlanbook.com/mac-os-x-wifi-scanner-snow-leopard/
Have you tried updating the router firmware .
Please provide a model number , and i will find the firmware download if any .
Are you using any bit torrent clients on the network , Vuze, bit torrent etc , lowing connections within the application settings can help a cheap router not crash under load .
Please reply using Firefox , your browser is not supported on this site .
i.e bad formatting , i.e no carriage returns . .