Hey a newbie! I ought to toss out something that's been on my mind, about the registration process becoming the board's demise, but I'll focus on the problem at hand.
The nuetual safety switch may be an issue, but I wouldn't know how to go about verifying it because if the switch has an intermittent issue, it can cause a no crank in neutral. If there is a way to bypass it, that would be one way to conduct a long term survey.. (My car's switch was failed in 77 before I bought the car. In all the years, it has never been an issue because I use certain protocall when starting a vehicle.)
I would also focus on resistanc and ground issues. I always start at the begining and work back. Have you checked the battery terminals to cable connections? It never ceaases to amaze me at how many dirty battery-post-to-terminal conections have been the root of the problem. In turn, I have heard that the connections are clean, yet they are filty, and the reports come from people of whom seem to be quite knowledgable in automobile mechanical issues. Clean means that the surfaces look like chrome, not the absence of white crust. If the mating surfaces don't look like chrome, they are filty and create exponential resistance. Ditto for ground connections.
If that's in order, it can be narrowed down as the neutral switch being suspect.