I am still not totally clear about your problem. Does the engine rotate when you turn the ignition to the start position or does it do nothing?
It would definitely be highly unlikely that the computer module is the problem.
The air in fuel problem mentioned is related to the fuel filter housing not the fuel pump.
For future reference, the transmission module is separate from the main computer module. Transmission module on passenger side computer module on drivers side. The transmission module is not vehicle or year specific any module from 05 or 06 Jeep liberty diesel sold in US is compatible.
If you need a module it would need to have the vin number of your jeep installed in it. GDE can do this for about $50 and shipping with very fast turn around probably 4 business days or less. Here is a link to one on eBay right now and you could probably have it shipped to GDE directly to save time.
http://www.ebay.com/itm/TESTED-05-JEEP- ... O~&vxp=mtrAny 2005 US jeep liberty diesel module will work. If you want to confirm its the problem the ECM can be replaced without changing the VIN with any 2006 0r 2005 ECM and the engine will start and run for a few seconds normally then cut off. ,but only the 2005 module can be used as permanent replacement.
You need the codes badly. There are codes for communicating problems with ECM these could be related to many causes such as bad grounding wire connections.
I agree with others most common things if engine rotates but doesn't start are
1: air in fuel, bleed air pump filter housing
2: Fuel filter clogged or possibly water in fuel , warning sensor may not be working
3: Crank position sensor
4. Low voltage to ECM from various causes including Battery shorting
If You really want to confirm it is the ECM I have a 2005 one you could use for testing for a returnable deposit. I don't want to sell it but it would start and run your vehicle for a few seconds then you wouldn't be wasting your money on one if it isn't the problem which I suspect it isn't. PM me if you want to consider this.
Also its highly unlikely anyone but GDE or a dealer would be able to change the VIN number in a ECM module to work permanently with your vehicle.
Many able and willing to help here but need more info.
Good Luck, Hope its just air in fuel.