Do both cars have a security pellet in the key? If so...switch pellets. Usually a car with a mis-matched key pellet will start and run for a few seconds then shut down.

Do you hear the fuel pump running when you switch the ignition on? GTP fuel pump wiring is different with a two-speed relay circuit and your GT doesn't have that relay or the wiring that the GTP PCM is trying to use. If I remember right, it runs the pump at high-speed until the engine starts and runs.