Hi I'm Dave.
I have seen this issue many times. It happens on several Saturn and GM models (they all use similar shifters).
The problem is there is a micro switch that gets stuck in the shifter assembly. There is no adjustment for the switch, and I have been unable to purchase just the switch itself. This results in having to replace the entire shifter assembly.
This is not a really hard job. About a "zillion" screws, 4 nuts, disconnect the electrical connectors and the shift cable, and the entire shifter comes right out. The shifter assembly is surprisingly inexpensive (not nearly as costly as I thought it would be the first time I ran into this problem).
For illustrated instructions on how to make this happen, download the PDF file HERE
The file will be deleted from the file server in a few days due to copyright restrictions, so you might want to save a copy to your computer for future reference.
Bonuses are greatly appreciated!
Let me know if you need further assistance.