75 Duster Neutral Safety Switch... I need to replace it!

The ballast has nothing to do with the starter circuit, that's the ignition circuit. Don't spend money there at this point because the car doesn't turn over.

Does the starter kick over when jumping the relay on the fender?
Check the NSS switch plug as mentioned above.
Disconnect the shifter linkage from the bottom lever, there are two levers, top is kickdown, at the trans. When you disconnect the linkage, observe if the linkage wants to, has play to move rearward. Move the lever all the way back, that's park. See if the car will start, move arm two clicks forward, neutral, see if it starts.

If the linkage bushing are in bad shape your NSS may not be getting activated by the trans internals. You mention slamming the lever into park and the car will turn over. That's a symptom of bad bushings or misadjustment.