Starts up fine, then dies ...

all in the link

https://www.google.com/search?q=Firing+order+diagram+2004+Jeep+Grand+Cherokee+limited+4.7

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Sounds like the relay that runs the fuel pump. The computer may be reading no oil pressure and shuts the engine down Check the oil pressure when it starts with a manual gauge. You may need to prime the oil pump.

Not me! But I digress. It seems that the cold start heater is stuck or broken...check it out.

judging logically by what you mentioned I would check the oil pump first.

Hi there cristina bam! If the core was bad it may have been leaking. Many newer cars on the road these days have a sensor specifically made to monitor the coolant level. If the collant has leaked out there is a very probale chance that the sensor is preventing your Jeep from starting to prevent damage. Add enough fluid to the coolant system to fill the motor block and radiator. If it starts it was the fluid level, if not, there is a greater underlying issue at hand. I really hope that this helps you out and if i was of some assistance please rate my solution. Have a great day!

hi i think its the camshaft censer

My 2000 Grand Cherokee had the same problem, without all the sputtering, it would just die approaching a stop. We could only keep it running by slightly pushing down on the gas petal when coming to a stop. I replaced the Throttle Position Sensor, but that didn't change anything. A new mechanic I found replaced the Idle Air Control Valve, and we've had no problems in a week.

You might want to start by replacing the crank sensor first.

can you tell me if you have problems starting the vehicle?

have the alternator regulator and diodes tested. sometimes when the regulators fail they allow ac voltage to go to the battery. ac voltage doesn't charge the battery properly (causes it to deep cycle and shortens its life) and causes all sorts of funny problems with the car. also make sure the battery is secured properly, vibration isn't good for them at all.