Every so often I will get in the car and the engine will turn over but the engine will not start. The "security" light will come on and as long as the "security" light stays on (possibly for 10 to 30 minutes) the engine will not start. It acts as if the fuel line has been shut off. As soon as the "security" light goes off, the engine will start and runs fine. This will happen only once in 5 months or as recenly as 2 days apart.
Ocasionally, the engine won't start and the "security" light comes on. on 2000 Oldsmobile Alero
I have the same problem and have found that it is the ignition lock that needs to be replaced. Got a quote of around $500 to repair, get new keys and recode the key fobs.