Q: What does the car do when anti theft is activated? does it have no compression kind of like head gasket?

The head gasket and/or other mechanical components of the engine are NOT involved in this fault you are experiencing, at all. Cavaliers have quite a few electrical and instrument panel problems. If you search the NHTSA database for complaints from owners of the 2004 Cavalier, you will see close to 200 complaints for just electrical problems on this model which is a very substantial number in my experience. There is likely a problem with either the ignition switch, dash cluster (which integrates the antitheft electronics or at least some of it), or both. In fact, the problems with the dash cluster are so commonplace there is a "cottage industry" out there rebuilding these clusters for consumers. Search on the Internet using the string: "rebuild cavalier dash cluster". If you have a passkey type security system, you can try this procedure: Turn the ignition key to the ON position (NOT start). Attempt to start the engine, then release the key to ON and leave it there. The vehicle will not start of course. Observe the SECURITY telltale, after approximately 10 minutes the telltale will turn OFF. Turn OFF the ignition, and wait 5 seconds. Repeat steps 1 through 4 two more times for a total of 3 cycles/30 minutes. The vehicle is now ready to relearn the PASSLOCK Sensor Data Code and/or passwords on the next ignition switch transition from OFF to CRANK. The vehicle learns the PASSLOCK Sensor Data Code and/or password on the next ignition switch transition from OFF to CRANK. You must turn the ignition OFF before attempting to start the vehicle. Finally, start the engine. The vehicle has now learned the PASSLOCK Sensor Data Code and/or password. If this procedure does not work for you, or you want a certified Mechanic to walk you through it, the service to request is a no start diagnostic. If the above procedure does not work, there are other bypass procedures and, as noted, the possibility of an ignition switch and cluster fault will have to be diagnosed. If you request a no start diagnostic, the responding certified mechanic will walk you through all of this. Please let us know if you have further concerns or questions as we are always here to help you.