95 riv starting prob

my riviera won't start all the time. You can go out and try to start it everything turns on but it just won't even try to turn over. Like if the battery was dying. I replaced the battery and spark plugs and had the starter tested and it passed. I am getting fed up. Should I try to replace the coil packs? How do I know which one is bad? Or is there another way of fixing the problem without having to take it in. There is no check engine light. Non S/C

Do you have a security light on while trying to start?