If it's connecting to the router but not to the internet, make sure that your router is connected to the internet. Use some other device(a computer, laptop, etc.) and go to some link - here, aol, anywhere.
Check that the CC's IP address (in the CC - I don't have one, so I can't tell you how to do that - look in the manual if you don't know) starts with 10, 172.16 to 172.31 or 192.168. If it starts with 169, then no matter what it says, it's not connected to the router, it's generating a local link address.
Make sure your router can be connected to by some other device (one in addition to the ones that are already connected), and make sure that device can access the internet. Then turn that device off and try to connect the CC. (If there's no available DHCP slot, no device will connect.)
Make sure that the CC is set for DHCP or Dynamic IP address, not Static IP address.
Those are the first things to check.