You have to power down the cable modem, swap the cable and then power up the cable modem. As to the router there are too many other reasons so I can't list them but the move the cable issue? Well known.
I was told that the Internet connection is much faster if I connect the Ethernet between the modem and TV so I tested it out. I unplugged the Ethernet that connects between the modem and Airport and plugged it in directly into the TV's LAN. Immediately, the TV alerts me that a network cable has been connected and asks if I want to connect. I click on start, but there is no connection. I don't know what else to do.