The transponder inside a PATS Key.
I decided to throw caution to the wind and take the Mustang out to do some chores. I made many stops and the car started each and every time. I had my cellphone and AAA auto club card with me just in case. I thought I'd state exactly what I did just in case someone else is searching the net for an answer to their Mustang key problem.
This is what I did to reset, or pair my PATS key with my car after the battery had been dead in it for months:
1.) Put key in ignition and turn it to the on position, don't start.
2.) Wait 10 minutes for the the Theft light to go out, it may go out earlier, just make sure you wait more than 10 minutes total.
3.) Take key out of ignition.
4.) With your remote key fob, lock and unlock the car a few times.
5.) Put key in ignition and turn it to the on position, wait for the Theft light to go out, then start the car.
Here is a video that helped me. https://www.youtube.com/watch?v=X_kUlojMdYw
His car is a New Edge Mustang, 1999 - 2004. Mine is an SN95 Mustang a 1998. Just be warned that this might be just for the '98 and up Mustangs. My wife had a early 1998 Mustang and the key was different than mine. My car was made in Oct. '98. Hope this helps anyone that is stuck.