I think you can forget the idea of a code in the OBD II system. There is no sensor to tell it that the key didn't turn on.
But, the test I suggested above should tell you if the switch isn't turning far enough to make contact with the start circuit contact. If the switch is turning only to the ON position and won't turn any further, you have a mechanical problem in the switch assmbly. Mechanically, the shifter must be in park or neutral. This alignment will allow the switch to turn to the start position. There is a pin, or flat, or rod, or slot, etc... something associated with the shifter that obstructs the switch assembly behind the key cylinder in all other positions. That blocking part has failed in some fashion which prevents turn to start.
If you could get your hands on a shop manual, you might get more details. The local library might be a place to start.
I have two Haynes manuals that cover Chevrolets through your year and neither has details about the mechanical stop item. Each tell how to replace the key cylinder, but not much else. The pictures showing the ignition assembly didn't show much either. If you drop the stearing assembly down and remove all the coverings from it, you might be able to see how it works and fix it.