ignition question?

Twice in the last six months the car has failed to turn over when started for several minutes instead of firing right up. Today, when it happened, I noticed the security light was blinking inside the dash although the theft alarm obviously was not on becuase I was IN the car. My question is could this be a computer(electrical?) probem becuase I am wondering if the car will or will not start if the security system is on. I wonder this becuase as soon as the security light went off, the car started fine. Has anyone else experienced this?