94 Toyota Camry won't start regularly

I have a 94 camry which has had intermittent
starting issues over the past few years. Replaced
starter, starter relay, battery, and battery
connectors 1.5 years ago. It has occassionally
acted up. Mostly when it is extra cold in the winter.
Not starting. Doesn't turn over.  No sound. Lights
and radio work. Doesn't take a jump. Sometimes it
will start right up when in between a gears. (Ie -
when pulling just out of N towards R).

Recently it died after sitting for 24 hours on 90
degree days. It is currently not starting. I have
charged/tested the battery and it is good.

I am wondering if there is something wrong with
the neutral safety switch? Is there an easy way to
test this? What are my other possibilities/options?