I have a 2000 7.3L f-350 and my truck did the same thing. If I ran the rpms up when I first cranked it would pick up and keep running. If not it would run a few seconds and cut off I then had to pour oil in HPOP to get it crank.When I took it to my local Ford dealer they said to replace basicaly everything involved in it from the HPOP to the injectors with a $3, 000 estimate.
Luckaly a freind was taking a class on the 7.3 and asked the instructor who said to replace the base pan oil pump eventhough the oil pressure was good.
I did and have not had a problem sense and that was about 2 years ago.