@Mbrooks420,
@imp -Yes I was referring to why the Ford stealership couldn't diagnose/fix this one specific problem, not PATS in general. Furthermore I'm talking about Gen II PATS only. I know nothing about Gen III PATS, nor is it relevant to this conversation.
Personally I've never experienced a PATS problem other than why my '01 Sport Trac will sometimes do weird stuff, like flashing it's lights on/off for 5-10 seconds for no apparent reason, which is somehow related to using the remote key fob (which is also not relevant).
Definition - PATS code flash 1:3
Key code not received. Is key screened by other keys or objects? Try different key: if okay then first key is faulty. If not go to main dealer...
The OP's transceiver ring may be reading the key code and the PCM has the key code(s) stored in it, but it sounds like the key code is not being sent to the PCM. If this is the case IMO it could either a wiring issue, or that something got/is shorted out. The transceiver is supposed to read the key code and send it to the PATS module (which I have heard described as a dumb bus). The module then sends the code to the PCM, which can be programmed to recognize up to 5 key codes. If the PCM recognizes/verifies the key it turns on the fuel injectors allowing the engine to start. To my knowledge this is how Gen II PATS works. No fuel pump control, no starter motor control, no spark control.
As the OP's original transceiver ring was damaged during the attempted theft, it seems logical to me that there may also be wiring damage and possibly that something was shorted. I would begin by checking
every fuse (not just the ones that seem to be protecting PATS/PCM related circuits) and all the wiring related to the transceiver.
IMO the Ford mechanic doesn't know what he's doing and/or they can't be bothered trying to fix the problem, so they tell you it's going to cost $1,000 to fix it hoping you'll just go away (or buy a newer car). At this point in time all the knowledgeable Gen II Ford mechanics have retired or moved on. We are talking about a 20 year old vehicle here.
If this was my vehicle and I couldn't find/fix the problem myself I think I'd go the route paying $60 to having my PCM modified to turn PATS off.
OP - I guess PATS did it's job, as your thief was not successful in stealing your vehicle.