1995 Buick Regal GS Ignition Problem

My car has a starting problem,I have changed the starter twice and since then it has run fine.......until now, It has the 3800 motor.I've had the security system checked,ohm's in the keys are good,all fuses are good. I'm confused about this,some say the neutral saftey switch may be bad,and there is 2,ignition switch may be bad,who knows? If you put a screwdriver across the solenoid terminals it turns over but wont stay running. The battery has a full charge and we eliminated lots of "what if's"....anybody have any ideas? I appreciate the help! Thanks! Ray

I assume when you try to start the car, the engine will not turn over. If this is correct, when you turn the ignition switch to the on position, do you have a security light on? The resistor in the key is only a small part of the security system!