Just swap the fuel pump relay with the horn relay, just for testing purposes. If that would solve the problem and the horn still works ok, then you are all set.
Didnīt know that you already changed the PCM. The problem could well be there as well.
JEEP Grand Cherokee 4.7 Lmtd 2004
HID 8000K in low and fog / Quad Squad member
KYB Gas-a-Just shocks / Pirelli Scorpion ATR 245/65/17 - Transgo reprogramming shiftkit.
I went to check the fuel pump relay one more time before the pcm came in. Popped it open and the relay was completely out. Pushed it back in and runs fine. Must have been the o2 sensor after I fixed the relay. Running fine now. Thanks