I have a craftman garage door opener that is not working properly. The green light on the wall controller sometimes on and sometime off. When the light is on, I have no problem opening the door. However, when the light is off, I cannot open the door either with the wall controller or the remote controller.

This sounds like a loose connection to me. Check the screws on the back of the opener where all the wires are. If that doesn't help, I would next pull the wall controller off and check the connections there.

Best of luck,
WallyH