Maybe I'm confused. There's OFF, I, II and START, or four total positions. I presume position #3 as described equates to START, so if it turns to 3 (or START) where else would it go? Or is OFF being referred to as #1 instead of 0?

There's a note in the manual that says "starting mid-78, a modified repeat start lock is installed. With this switch, the time limit is extended, since the key must be returned back to "0" prior to a restart (up to now position "1" only). Did you go all the way back to Off, or just to 1?

Or maybe the ignition is working correctly, but corrosion described when jumping is stopping the starter from engaging?

Off - the steering lock can engage;
I - it can't, and this is the "accessory" position;
II - it can't and this is the "run" position;
START - it can't stay here since it's spring-loaded back to II. If it can't get to START, I don't think that's the tumbler's fault, but is the ignition switch fault.

However, having seen the drywall-screw-in-the-ignition "fix" that the PO for my car installed, I wouldn't be surprised at almost any mode of failure in the ignition and/or tumbler.

VIN matched tumbler and key is closer to $100 from the dealer. Need to show title as well. But it keeps you with single key for doors, trunk, ignition, and assuming your current key(s) are good, you already have spares.