Here's some more weirdness that I've noticed:
With the key in the ACC and ON positions, everything is mostly normal except that the car won't start. No clicking of the solenoid or even attempt at starting. Yes, the starter is plugged in, the hot terminal is tight and the blade connector is connected. I even checked to see if the battery was just dead by jumping it, no dice.
With the key in the LOCK position (i.e. off) weird **** starts to happen. The headlights stay on, all of the back lights on the dash are on, the wiper lever activates the cooling fan, and turning on the turn signals appears to activate the ABS (I'm assuming this is why the ABS light is coming on). It does this regardless of if the key is in the ignition or not.
Are there any ideas?