I think you're a bit confused about addresses.
When a router and computer don't talk, it's usually because the router is tied to a specific MAC address, the hardware address that belongs to your network interface, whether Ethernet or AirPort.
However, power cycling the router usually fixes that issue, which means the next problem is you aren't getting an IP address from the router.
I don't know much about the Qwest router you're using - what kind of router is it?
If we know that, I or someone else here may be able to help you further.
In theory, the router after a power cycle should just recognize your new machine and assign it an IP address, but if you go far enough back in time some ISPs required you to register the computer you were using with the ISP and their device would only issue an IP address to that device.