mercury 2000 grand marquis won't start.

I previously posted the same question, and got one answer, which was helpful. However, I now have additional information. The car cranks, starts to run, then shuts off with the antitheft light on the dash flashing rapidly. The dealer claims to have replaced both the PATS module and the PATS transceiver. They also refer to the problem as Intermittent, which it was not, since the failure had become solid and I had the car towed to the dealership.
They say the next thing to try is diagnose the PCM and fix it. It's not clear whether they mean replace it or reprogram it. I'm already out $540 and am getting worried I'm going to be spending big time money before this is all done. I can use some guidance from the experts.