1995 Oldsmobile Aurora engine cut off

most times when i put the key into the ignition i will hear the fuel pump come on and the car will start. But, sometimes when i put the key in and turn the ignition, i do not hear the fuel pump and the only light on my dash is the security light. I retry and sometimes it takes several times before it will start. It seem after this happens I will be driving and the engine just cuts out i pull over and restart it. No jerking, or stall action, it just shuts off. I had the resistor in my key checked and it it fine. Any ideas what this is? Maybe a relay? faulty switch in the ignition? Any help would be great!