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Does it start fully, then shut off? Is there a symbol on the dash with an outline of a car with a key in it? Did this just happen, or has your check engine light been on?
It could be any number of things, but since it does start before dying, and since you have had a prior check engine light, I am thinking you are having issues with the high pressure pump. The only way to know for sure is to start off reading your fault codes, which should give you some direction to go. If it seems to be fuel related, you are going to want to check fuel delivery pressure from the in-tank pump, and then remove the high pressure pump and check for damage to the cam follower and the camshaft.