As said, the immobiliser is fine. as long as the light comes on and goes out.
If the immobiliser wasn't working the engine wouldn't even crank (From experience removing the code box fuse on another car).
Try pressing the fuel cutoff button in the passenger footwell. My 145 used to occasionally trip this switch when I did engine work. If not, probably the Crank position sensor.
Final possibility is a flooded cylinder which I experienced on my sisters honda. Same symptoms, engine would just turn and not catch. The fix for that was to hold the throttle wide open and keep cranking. After 30 seconds it would start with a lot of smoke.
Alfa GT 3.2 V6 - Daily Driver.
Alfa 145 QV ph1 in green (Death by rust project) For Sale.
Alfa GTV TS ph2 in blue