I would see if you have voltage to the coil. there should be a DK GRN/BLK wire that runs from the the alt to the coil,Injectors, the ECM, the auto shutdown relay and the Heated O2 sensor. You can swap around relays to see if they make a difference if they are the same type. The good ones give you a picture on the side of what they do and if those match you are good to go.
Obviously the coil circuit itself is simple. the Wire from the alt comes in and the ECM acts as the ground telling it to turn on. You said the coil is god so either the wire in is bad, the wire to the ECM is bad or the ECM is not telling it what to do.
The ECM is new so for the sake of troubleshooting let's assume it is good, especially since it sounds like you got it to fix the problem. In that case something is telling it NOT to turn the Coil on. Of the thing that would probably tell it not to turn on the coil are. The Auto shutdown Relay, the Fuel system Relay, there is a another wire from the alternator that is TAN/BLK. I would make sure all of those are functioning or connected properly.
The IOD, if used in the same context as other places is the Ignition Off Draw. This is things like the Clock, the radio, alarm system and anything else that pulls current when the Jeep is off. Usually those pull milliamps so not enough to blow the fuse. When you say you have a short on those are you testing it, is it a diagnostic code or are you basing it on a blown fuse?