1995 Chevy Lumina no start

My daughter has a 1995 chevy lumina sedan 3.1 it sometimes will not start when this happens it will do nothing when you turn the key. When she keeps trying then it will usually start.I have tryed the other keys we have, I have tapped on the starter no luck, I have checked for power at the starter solenoid when the problem happens and had no power at either terminal with the key in crank mode, there was power to the starter from the battery. I replaced the ignition switch thought I fixed it, but did not. 3 yrs ago I had replaced the park neutral safety switch for a similar problem, but the car would start when you wiggled the shifter at that time. Do you have any directions to lead me in? Thank