1999 Pontiac Grand Am Ignition/security light

Occationaly I will attempt to start the care and the engine will crank, but will not turn over. The security light will come on, I then wait and in approx. 10 min. The car will start. Recently this is happening on a more frequent basis. Considering the model, year and mileage which component is the culprit: The Ignition switch or the key cylinder and sensor? How would I test both? What would you try first?
FYI
This problem has happend with 3 differant ignition keys. Also, sometimes the security light will come on when the car is started and will remain on for the whole trip. The next day the car starts fine and the security light is off.