2003 Chevy Cavalier Intermittent Start

Having issues with car starting. Sometimes it will start but then you turn it off and it will not start. The ignition engages but the engine never fully turns over. Have also had incidences where I am driving and car would die out of nowhere. No signs, noise or anything just dies. Engine light isn't on. This car is pretty basic. Fuel filter has been replaced as well as plugs and wires and recent oil change. Prior to the recent work the car would occasionally not start upon intial start but once turning key to off posistion and attempting to start again it would start right up. Seems now the issue has just gotten worse. The car is in the shop and mechanics can't figure it out. I have read something a an Anti Theft light. Never heard of this do all 2003 cavaliers have this? I would check on that but car isn't here right now.