A signal issue is occurring somewhere between your receiver and the Cox server after you've started watching a channel. When you press the channel up, channel down, or any other button on the remote that requires communication with the Cox server, the Contour receiver locks up waiting for a response that it never receives. That signal issue is also the reason you're unable to restart your system until it's cleared up. The same thing would happen if you were watching a recorded program and pressed pause, fast forward, reverse, etc.
You need to schedule a tech that can check your signal strength, including at the pole. (Ask for a tech with a long ladder). You can't schedule it for evening hours, so try to schedule it for as late in the day as Cox will schedule an appointment.