2001 Chevy Impala Car Won't Start at Certain Times

My 2001 Impala has a lot of miles on it; but the problem is - sometimes when I go to start the vehicle it won't kick over or start. The radio and interior lights are all working it just won't start. The Security light also flashes when this problem is occuring! Sometimes we shift it from park to reverse to see if it's stuck and after a few times and just letting it sit there for at least 15 minutes it will just decide to start like nothing was wrong? Could it be anything with the gears and shifting or maybe a sensor that's telling the vehicle the car isn't in park?