Since the key comes out when the battery's disconnected, it's the interlock.

That's a system where it won't let you take your key out unless the tranny is in Park. Somehow, the system doesn't 'know' the tranny is in Park. Usually that's a flaky switch down at the shift lever, but in that case the "P" wouldn't be lit up.

Can you get your hands on a wiring diagram for your year? Maybe you have to check wiring to the ignition lock cylinder, or other connections in that circuit. Maybe there's a relay messed up in that system?