though a late xj40 , it shared a lot with the x300 model , and i had exactly the same starting issues ( or lack of ) as described above
the body module would indeed prevent the car from starting, as part of the fault finding i manually operated the starter motor circuit in one of the under dash relays, the car started and ran , the signal to make this work normally came from the BPM , i eventually obtained a replacement of the same model number ( there are a few ) and ensuring everything was grounded correctly with the battery disconnected i swapped over the modules and in my case the car then performed correctly ( i now keep a spare just like the CPS )
the good news is these modules are fairly cheap on ebay , but buying in your country may be difficult, and its a ' punt ' to be honest, as mentioned above, fault finding diagnosis is the correct way , but is time consuming and very expensive from an auto electrician etc
best of luck
if not confident , then do not do this, i opened up the under dash relay module with the starter relay circuit inside by removing its lid, and manually depressed the relay contacts inside to start the car with the ignition on , it fired and ran , THIS WOULD BE DONE AT YOUR OWN RISK.......
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