It really depends on your setup, but (default) router settings and Xboxs are designed to run in parallel without any conflicts.
This error code is from you trying to connect to Live? Do you have computers connected to this router? Do they connect to the internet when the console is showing this error?
If you do have a computer connected to the router, go to Start>Run>cmd
In Command Prompt, type in ipconfig/all, take a screen shot and post. Be sure the screen shot gets all the data that ipconfig/all spits out.
On your Xbox, are the network settings configured manually, or are they set to automatic?
Navigate to the Network Settings>Configure Network pane and list off what the Xbox has listed as its IP, Subnet Mask, and Default Gateway. Also include your DNS settings if the first entry doesn't match the IP of the Default Gateway.
Hopefully we can get this worked out for ya.