Carb or injection (89? is when they switched to injection)

Whats the idle speed set at? Should be set with the car running, in gear, with the vaccum system plugged, 700ish rpm.

What happens if you rev it to 1200 rpm, and put it into gear? (do not apply brakes)

I think you have 2 issues. 1 being a dead neutral safety switch (known weak point on the fox bodies) , 2 being a finky motocrap or edlebroken carb.

Door number 3 is unlikly, but POSSIBLY the transmissions having issues like a dead torque converter. How did the car drive before u shut it off, and whats the fluid level/color/smell?
~Nate

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95 Honda Shadow ACE 1100.
1999 Plymouth Neon Expresso. 2.4 swap, 10.5 to 1 comp, big cams. Autocross time attack vehicle!
2012 Escape, 'hunter" (5 sp 4cyl)