I gave my son my '92 Bonne (120,000 miles) to drive to school. The other morning he tried to start it. It would not turn over. I tried a couple of times with my key. It would not turn over. All the dash lights come on with the ignition in the "on" position, etc. Reading some prior posts has confused me about VATS problems. (What does VATS stand for?) If it doesn't recognize the key, will it let the engine turn over anyway and just not let it start? Does the security light remain light after you try and start but turn the ignition to off? The security light did not stay lit.
Anyway, after trying a couple of times it finally started. I turned it off and restarted it several times. It'* worked fine since. I also cleaned the keys and switch based on what I read on this board.
The battery cables and connections seem fine. I didn't get a chance to get under and try and jump across the starter terminals with the switch on.
Could this be a neutral start switch issue? The car reacted just exactly like trying to start the car in gear. Is it the same switch if you are in park or neutral? My suggestion to my son, if it happens again, is to wiggle the gear shift and shift to neutral.
Any other thoughts/things to try??

VATS = Vehicle Anti Theft System
I believe VATS shuts off the fuel if it does not recognize the correct resisitor value, so it will crank but not start. Check the pellet. The metal contacts could be worn level with the pellet and making intermittent contact. Do an internet search for "gm vats". There is much information. Try this one for starters. http://www.asttraining.com/Files/vats1.pdf

You can check the neutral saftey switch by moving the gear selector while the key is in the crank position. If you find a spot where it will crank, then the switch is bad or out of adjustment.

Check the cables. Not only for tightness but corrosion inside the cable insulation.

Thanks. The link indicates it'* a no crank condition if the VATS is bad. I'll check the battery cables a little closer this weekend.

on a similar note if the VATS system detects infinite resistance (IE severed wire) the car also will not crank, but the security light will not stay on. Instead, with the ignition on the security light will flash but the engine will not crank. If the VATS system detects a value of resistance that is not infinate but does not match what it should be, then the VATS system will not let the car start AND the security light will stay on for 3 minutes after the ignition is shut off. In this 3 minutes that the light is on the car cannot start even if the correct resistance is seen. This is to keep someone from trying all of the 13 possible resistor possibilities as quickly.