Ok, for anyone reading this thread in the future:
1) Switching out the ignition switch fixed my problem. I was able to start the car (eventually). There are a lot of tutorials and threads out there. I think this was probably the best:
https://www.pelicanparts.com/techarticles/Porsche_997/Ignition_Switch_Replacement/Ignition_Switch_Replacement.htm
I know this article is for a 997.2, but the procedure is the same for a 997.1.
2) The ignition switch is held in place by a zip tie that is anchored down. Some people carefully cut the zip tie. I carefully reached under it with a flat head screw driver and pried it up. If I had to do it again, I would try a trim tool first.
3) No key coding is required.
4) The special VW trim tool is not required. I used a generic trim tool to slide it around and unlock the ring holding the ignition switch in place.
5) Don't get discouraged if the car still struggles to start. My battery was drained to near zero and couldn't hold a charge. A portable battery kit could not start it. Finally, I hooked up jumper cables to the mighty family minivan, let it charge for good 15 minutes and was able to start the car.
Overall, I'm pretty happy. I don't have to tow the car several hundred miles to a dealer and I got it running by myself. Thank you to everyone on this (and other) message boards who posted enough information for me to fix it.
The zip tie holding the connector cable into place.
The hole inside the dash that the connecting cable is locked into.
