Do a search, there's a good bit of info about the EDIC operation here.
Easiest check to do: have a helper watch the EDIC arm as you start/run the engine. It should move to "O.I." (to the rear) while the key is in start, then move to the venter just running, and watch what happens after that. If the engine just dies without the arm moving, then it may not be an EDIC problem. If the EDIC moves forward and the engine shuts off, then the EDIC is shutting it off for some reason.
The EDIC will shut the engine off if you turn the key off, or if it does not detect oil pressure (except for shortly after the key is in start, in which case it inhibits the oil pressure shutoff for a few seconds).
If the EDIC is shutting it off, try unplugging the oil pressure switch wire, and see if it still acts up or not. The switch just grounds out the wire when there's no oil pressure, which is what commands the EDIC system to shut the engine off. So if you have a short in that wire, or the switch is stuck closed the engine will never "detect" oil pressure.
I would personally not do any of this without a working oil pressure gauge though. At the least, go buy a cheap mechanical oil pressure gauge just so you know you've got oil pumping through the engine.
Dan