Go and buy a cheap voltmeter (or borrow a friend's) and trace the circuit to see where you are loosing the starter signal.
Battery power is fed to the ignition switch pins 3 and 5 (sounds like you have power here). Power comes out of the switch on pin 2 (violet wire) in the start position and goes to pin 8 of the park neutral switch and out at pin 6 (violet/white). From there it goes to the starter solenoid. This is a simple series circuit, so a break anywhere in this string will cause your problem.
Some cars have a relay in the circuit as well, but the manual does not show one for your year and model.