All models got an immobilizer, there is a transponder inside your ignition key and an antenna around the ignition switch (prevents the key from being copied). The LED on the left front speaker grill will flash while the car is off (that is on the very early models, also LED on radio, later models might have different LED). If you turn the key and it still flashes, then the immobilizer is not working. I can not remember if the immobilizer also disables the starter motor, I would think it should. But anyway, the problem is most likely related to the fuel pump relay.

Easiest check to see if it is the pump is to connect a bulb across the fuel pump terminals. If the pump does not prime but the bulb lights up then it is the pump that is faulty.

To diagnose the relay you would probably just replace it.

Did you buy the car new? There might have been an aftermarket alarm installed and that alarm is gone faulty (or botched-up wires).