The following are the main components of the Cruise Control System: The accelerator pedal
The stop lamp switch
The body control module (BCM)
The cruise control switches
The engine control module (ECM)
The throttle actuator control (TAC) motor
The vehicle speed sensor (VSS)
A fault in any of the above components would cause the problem described.
One of the most common cause for the cruise control not to engage would be an out of adjustment or faulty brake switch. I would suggest starting from there.
System is equipped with self diagnostics and a scan tool would help to chek for trouble codes and assist ini resolving the problem.