I don't know the 'ins and outs' of the diesels, but sometimes on car injection systems there is a check that the engine is running that the ECU has to detect in order to keep the engine running, and this is bypassed during the starting routine, which can be detected by power being supplied to the starter motor. When no power is supplied the check on whether the engine is running or not is applied. If the sensor or whatever is giving an indication that the engine is not running the fuel supply is cut off. So your engine starts but as soon as it starts and the starter motor is shut down, the engine stops within seconds.
This was the case on an old Jaguar XJ6 I once had which had an early fuel injection system, (Bosch L-Jetronic) and analogue system. The mass airflow box which had a flat valve that moved as the air entered the inlet manifold and had a pair of contacts in it that were closed by the flap once the air started passing and this kept the fuel pump running. It was bypassed during starting with, (I think), a relay. There was some safety issue that had resulted in this arrangement.
Might be worth a look to see what checks there are in the ECU to determine whether the engine is running or not.
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