1997 Pontiac Bonneville Car won't start: security light fla

Today I stopped at the store and when I returned the car would not start. AAA checked the battery, alternator, starter and it did not appear to be any of those problems. My mechanic tried starting the car and he was able to jump it underneath, but it immediately shut off. The car thinks I am trying to steal it after I have had the car over 5 years! My mechanic is stumped. We tried swithching the keys and even tried leaving the ignition on for an hour so it might recognize the key. The security light had been on for a few months, not flashing, but just stayed on. But the car started every time and there was no diagnostic code when my mechanic tried to figure out why it was staying on. This is a complete mystery that has both my mechanic and I totally stumped. Please let me know if you have any suggestions or recommendations. Thanks, Steve