As i recall from past experiences with this car, there is a bypass module that you need in order to activate the remote start. This would have been installed in the car when the remote start was installed. To see if this is the problem take a key and place it into the ignition, next try to start the car using the remote start. If the car starts then the problem is with the bypass module. In grand ams we have had problems in the past with the transmitter rings being ineffective against the ignition harness. If you try the key trick it will at least isolate the problem. The next thing to do will be to take everything apart and move the transmitter ring into the correct spot.
Any more questions feel free to post again