ADT has been a well-known name in home security for more than a hundred years. Originally a telegraph company, ADT used its communication technology to form a security division. They expanded in 2010 when their parent company Tyco purchased Brinks' home security division, adding about 1.3 million subscribers to the ADT umbrella. ADT systems are designed to be activated and turned off with a few button-presses of a control panel so troubleshooting can normally be done with minimal fuss.
Check all your doors and windows if the system won't activate to ensure they are all properly secured. The system can't properly arm if a door or window sensor is ajar or it will result in a false alarm going off.
Examine the control panel to look for error messages. "No AC" means the panel isn't receiving power. In that instance, check the plug the panel is hooked up to in order to ensure the plug is working. If it is, unplug the panel for a minute and plug it back in to see if the error goes away. "Not Ready" means the system can't turn on, likely due to an open door or window, a malfunctioning sensor or a motion sensor detecting movement.
Press the "Reset" button on the panel to see if the system resumes normal operation.
Examine your motion detectors to verify that they are not facing windows or too close to heat sources. Both can result in false alarms.
Contact your phone company via cell phone if your ADT system is not communicating properly with the ADT call station to verify that the phone line itself is working properly.
Notify ADT of any further problems to see if the problem is coming from the monitoring station.