07 Rav4 wouldn't start: immobilizer?

[Dave52]

Anybody know of the key immobilizer? Wife started our 07; put in reverse and it quit. 4 restarts did the same but would only idle about 2 seconds before dieing. When I got there my key started it and then her key worked to. Anybody know how picky the key immobilizers are? She got a cell call the 1st time but wouldn't start after she finished. I know the manual gives some ideas. Toyota thought it was the immobilizer but has no way to determine what the problem was. Just wondering if anyone here has dealt with a picky immobilizer; if that was the problem. I assume the key code is only needed when the car is started?? Rav4 is 5 months old at 5800 miles.

Thanks
Dave