What could be the problem if your car won't start up. on 2004 Chevrolet Malibu

I tried starting my car this morning and it wouldn't start. I change out the battery, with a new battery. The car was hesitant initially but it started after a few seconds. I drove to work for six hours and return home with no problems. I let the car sit for three hours and the car refused to start up. I can hear the car turnover several times and it has power, the lights and radio comes on but it won't start up. What could be the problem?

Asked by for the 2004 Chevrolet Malibu
Could be a theft deterant system problem that is preventing it from starting. Next time it happens look to see if a "theft" light flashing on your instrument cluster. Car is at the age that passlock sensor could be failing in the ignition lock assembly.