I have a 96 ford E-350 with a 7.3 power stroke and it died it turns over fine. I did a koeo cylinder buzz test and its not buzzing the injectors it gives me a P-1668 pcm diagnostic comm err and when i just do a koeo self test it gives me a P-1663 fuel demand command circuit failure and a P-1667 cylinder indentification failure.If it sits for a long time it will start a run fine for a while then when you shut it off it wont start.

 

If you are saying it only starts cold & dies when hot ,,,could be a few things

IPR o Rings

Injector O rings

Loose poppet Screw

Worn poppet valves

If not ..

DTC P1668 and P1670 indicates that a communication error has occurred between the PCM and the IDM.
Possible causes:
open fuse
IDM relay
open or shorted IDM enable circuit
open/short in EF circuit
open/short in FDCS circuit
IDM powering circuits
PCM
Check for other codes.
Key on, engine off.
Perform KOEO On-Demand Self Test and retrieve continuous DTCs.
Was DTC P1668 present?
Yes No
If DTC P1668 is present, GO to U2 . If DTCs P1667 and P1663 are set together with or without DTC P1668, GO to U6 .
If DTC P1298 is also present, REPLACE the IDM.

If DTC P1667 is also present, GO to V1 .

If DTC P1663 is also present, GO to T1 .

If DTC P1662 is also present, GO to W1 .

If P1670 was set without any other DTC, GO to U10 .

 

I found it it was a open circuit in the idm wiring behind the battery repaired the wire and it starts just fine.