Could be the nuetral safety switch I'm not sure what Chevy had on that year but there is probably some type of switch on the brake pedal and another at the gear shifter to be sure it's in nuetral or park. Had trouble with an old pickup... The switch was behind the brake pedal lever above the brake pedal. I bent it with my winter boots and had to climb in an rebend it until it pushed when I pushed the brake in.
There is also some sort of fuel shutoff switch up under the dash on a lot of vehicles if it was in any sort of impact recently it could have tripped but seems to me the vehicle will still crank.
Could be the ignition switch is wore out too...
I'm not a mechanic but I figured I'd toss out my limited experience until the cavalry arrives.