If it’s the Hotwire car there are 2 immobilisers one is the green box 10AS unit which is operated by the key fob, the other is the “Spider” immobiliser which recognises the key itself, this unit interrupts the supply to the ignition system, can’t remember if it’s the coil or amplifier , these are very prone to dry soldered joints a simple bypass plug can be purchased online for around £10, Check the main & fuel pump relays are working ok and you have voltage to the coil, if you have to replace one of the relays make the New one is fitted with a diode.
If you are still having problems , there are 2 resisters in the loom to check
