The first thing I think of when people say "possessed" is grounding problem. A bad ground somewhere will cause the most insane problems.
When it will not start:
A: does it fire the spark plugs?
B: is gas being injected?
If there's no spark, ohm check the wires plugs and the coil.
If there's no gas, ohm check the injectors.
If everything checks out, it's got to be wiring, grounding or ECU.
OK here is the deal.... I drive my 1996 Jeep Grand Cherokee for a few months then it stalls and won't start. I tow the thing back home and it won't start for a week or so. It will turn over but will not start at all. So I wait a week or so and try it and the thing starts right up. The wierd part is that it will run for a month or so before it happens again. I have had it to several machanics and they can't find the issue. Even the dealer here was stumped. I have replaced every sensor on the thing, been through 2 computers, a transmission so I am done with pouring anymore money into it. Any body else hear of anything like this?