If the controllers are wired, then they might have a short in them. If wireless, the receiver may not blocked, or the controller similarly can't send signals out.
Check the connector points from the cable break, most times this is the problem. Otherwise your controllers are probably just at the end of their lives.
If your Xbox controllers are malfunctioning, then it may be a case of eventual wear, or more simply, loose wiring from the cable to the inside of the controller.
You may find that the reason that your x-box controllers won't work is that the batteries used in the controllers need replacing. A green light in the center of the controller is designed to flash repeatedly if the controller needs replacement batteries. To replace batteries open up the compartment on the rear of the controller.