On every occasion that I've used a "wizard" to set up a Cable/DSL router, at the end of the configuration it has always indicated that it can't connect to the internet. Nevertheless, it does work properly. I now always configure a router manually (by typing its IP address into a web browser).
Is the Router getting its correct WAN addresses (IP, Subnet Mask, Default Gateway and DNS Servers) from the Cable Modem?
Also, have you gone through the correct procedure for swapping a connection to the Cable Modem. You *MUST* power off the modem and leave it without power for several minutes so that it releases the association between the current connection (recognised by the adapter's/router's MAC address) and the IP address it has allocated to it). When powered on again, it will find a new connection and allocate a different IP address to it.