I think you're expierencing the same problem I have which strictly happens in the winter. I have a 92 LS Auto.

The quickest solution may be getting a copy made of your original key. I have yet to fix the problem myself so whether that'll work or not is in question.

From what I understand, G2 tegs are known to have a gear position switch issue. If the car doesn't detect that you're in the "P" (Park) position, it won't let you remove the key. The switch costs approximately $50-60 to replace.

Before replacing anything, play with the shifter when it's in park. Jiggle it back and forth, left and right and use the brake a little maybe. I've done all sorts of things but I often find myself sitting there for a good 5 mins.