Frequently when a non-factory alarm/immobiliser is fitted the original has to be disabled or removed. However this is not always the case.
I'd suggest checking the plastic shroud around the ignition switch/column for a sensor. The factory imoobiliser sensor (if one is fitted) has a tendency for the glue to let go, allowing the sensor to drop back down the column shroud and too far from the key for it to be effective. I presume no switches on the key fob?
Relays, if not where Dave W suggested, try up behind the glove box on the passenger side, you'll probably have to drop the lower dash panel to gain access, then emulate Cerealsurfer and Co. in one of their Morgan poses in the race car - i.e. inverted with head/torso in the footwell.
To me, it sounds as if an immobiliser isn't passing a 'Go' signal to the ECU.
Cheers,
