You might not be aware that a cable modem "remembers" the device that is used to set it up, so your modem is "remembering" your wife's laptop and it is still looking for the laptop when you connect the AirPort. The modem does not find the laptop, because the AirPort is connected, so it does not issue a valid IP address to the AirPort to allow an Internet connection.
The solution......your modem needs to "forget" the laptop so that it will "remember" the AirPort.
Power off everything on the network......all devices.....modem, computers, AirPort, phones etc......in any order that you want
Wait at least 20 minutes.......longer will not hurt, since some ISPs take longer to issue a new connection to the modem
After the power down period, start up the modem and let it run for 5 minutes by itself
Make sure that the Ethernet cable connects from the modem to the WAN (circle of dots) port on the AirPort
Power up the AirPort and let it run for a minute
Power up the laptop or another device and see if it can connect to the Internet
If yes, continue powering up devices one at a time about a minute apart until the entire network is powered back up.
If the modem still does not recognize the AirPort.....meaning that the AirPort cannot connect to the Internet......you will need to perform a Hard Reset on the AirPort and run through the process above again.
