Car will only start sometimes Please Help!!

I have a 96 Cav. 4 cylinder. My car will start sometimes, and when it doesn't the engine wont turn over gets no response. The lights are on but seems like its dead. I put the key in the on position and use a screwdriver on the starter and it kicks over and starts fine. I checked the battery, its still good, replaced the starter and solenoid and ignition switch twice, still having the same problems. Anybody have any suggestions. I'm going crazy trying to figure this out. Any help would be appreciated, Thanks

Do you have any type of alarm system?. Sounds like a short or a problem with one of your ground points. Also Welcome to AF.

John

Thanks for your response, yes i have and anti theft type chip that you can take out, when you leave your car. I never use it though. Not sure how i would go about disableing it.

If there are any other suggestions please let me know.. Thanks!!