Just a little extra info here... Its perfectly normal for an EDC equipped 300tdi to crank in the way the OP described.That the fobs worked to unlock the doors and the engine cranks shows that the fob/s are correctly coded to the alarm ecu. That it did not start was because it had lost the code between the alarm ecu and the EDC ecu.( In exactly the same way that used to trouble P38's - both petrol and diesel ) This code needs a reset with Testbook, Autologic or probably an older version of Rovacom. That when it also will stop running when keyed off without the plunger in the stop solenoid is also normal.The fuel quantity actuator in the fuel pump runs from no fuel to max fuel,so is fully capable starting AND stopping the engine.The normal stop solenoid was only kept as a backup.
Every time the fob learn procedure is carried out it cancels the coded link between the alarm and EDC ecu and will need to be recreated.. It is a couple of minutes work with Testbook, not done one for several years now...
 
Bit of a long shot, and I doubt it will work but worth a try.

Try holding both buttons down on the key fob for 10 seconds, then see if it starts.

I doubt it will work, but its an easy try, just read that someone tried this and it worked, but don't know if it the same fault as we have had.
Ha great, thanks for the info on the injector, funny thing about the key fob is that I’ve never had one. My uncle owned it as a fresh import way back and was never given a key fob.
 
Ah that explains how mine switches off as normal without the plunger in the stop solenoid, always did confuse me, as never expected that.
 

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