Ok. then this problem is with the security system. The proper way to diagnose this problem is by using a scan tool with the ability to read body trouble codes such as the theft system. This test will give you a trouble code that will further assist you to find the actual problem. I can tell you that better than 95% of these models have been fixed by replacing the ignition cylinder. The ignition cylinder houses the passlock sensor which has been a huge failure on all gm models. The problem is that without the scan tool you will be simply guessing. Simple obd2 scan tools will not be able to access the info needed to diagnose this problem. You MUST use one of the $3000.00 units like the pros use to get the trouble code. There is a simple releanr process that can reset the theft system and possibly allow for your car to run once again. Here is how to do that.
Important: The vehicle learns the PasslockTM Sensor Data Code and/or password XXXXX the next ignition switch transition from OFF to CRANK. You must turn the ignition OFF before attempting to start the vehicle.
Feel free to contact me with any questions! Good luck!