[AKITA]

a lot of people keep mentioning battery.. I think it has been significantly tested. (in fact I would say careful on the 2 car jumping.. some mechanics would say that's dangerous for the electronics.. and rather should be trickled charged from a car or device then tried to be started.. but hey what you gonna do in a pinch)

Has starter been tested to even work? maybe the pinion is wedged.

and if the starter does work... I gotta start looking at the immobilizer issue like you are pointing too.. because that much charge on teh battery should turn it maybe not start, but with the jump definitely should crank good. Alternator is not really the hurdle even if it's the culprit to the battery. I'm wondering too, you said you turned the key really fast and so I have to wonder if it is something in the ignition cyclinder got wonkered and set off anti theft. Since you replaced battery, I don't think its the key fob itself but could be for some reason (a wonkered key can do this)