I have read all of the above and still think its part of the automatic choke system which unfortunately is part of the engines black box (very expensive).

To insure its not your wires, simply observe your engine at dusk. If its a wiring problem, the sparks will light up from the point of origin (hole in wire, bad radio resister on spark wire etc to the top of your head gasket. However such a hole in a wire etc. would only affect the performance of the engine, especially during idling and not starting. In addition if it was some form of electrical problem, the injectors would still be letting in gas which you could smell at the exhasut pipe after some of the cranking you describe.

Also you never said that if the vehicle did start up at one of the "middle points" was there a bang or sudden acceleration (hydrostatic lock on the injectors).

Once you have eliminated the elecrical possiblity then the only other case is the throttling of fuel as the third part, lack of O2 would only be cause by a super dirty air filter or an old fashioned throttle plate.

A quick test would be to have a friend attempt to start the car while you placed your hand over the air intake and removed it after a few revolutions or until the car started. This test would indicate a black box interface with both the injectors and the spark unit, as the pumping motion of the piston movement would suck in more fuel if your hand is acting like an old fashioned throttle plate.

If there is a spark she should fire right up, but at the end of the day you still have a black box problem, which might be solved at the local junk yard. Incidently some of the folks in a junk yard are the best mechanics in the business, and might be persuaded to wire it up for pin money