So to recap René you have changed ignition and fuel pump relays and are fairly sure the immobiliser is working correctly. Can you confirm both relays click on with ignition switch? If so can you hear the fuel pump running for a short while when ignition is first turned on?
Note the the fuel pump control module (relay) near the tank that DaveW mentions can go open circuit which will kill power to pump (although it can be bypassed) but this is usually quite reliable though in maintaining fuel pump speed/flow against demand.
