On 1.9TDI's there is a common hot start issue that there is a map in ECU that has minimum rpm before start of fuel injection depending on temperature, I do not know exact figures but it could be something like 200rpm for cold and 300rpm for warm. If the battery or starter is a bit weak and engine does not turn fast enough ECU does not inject any fuel and engine does not start. The resolution is either new battery or starter or ECU remap.
I am not saying that it is definitely your problem as I have never heard it on 4.0TDI but then again it is not very common engine either. And the fact that you say it will start when jump starting could mean that starter is cranking faster when jump starting so worth investigating or trying new battery.
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Currently 8less
2011 Q7 S Line 3.0TDI, 2016 Tesla Model S 90D
8 history:
2006 A8 Sport 4.2TDI quattro SOLD,
1997 S8, reached end of life with gearbox failure
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