An update, some background and some further questions please:
I've done the easy stuff: the key solder all looks good. I've checked the internal fuse box for corrosion = none. I've also monitored the battery: After running for half an hour the voltage is 13.3 V. The morning after it is a steady 12.8V. Is 13.3V normal? It is higher than I thought. Could over-voltage be causing the immobilizer to freeze up the car, silently? Sorry, I really am a novice here. But I am thinking, it doesn't crank when the car has been driven for a decent run, but does crank after being left to stand overnight.
Some background is that immediately before this problem occurred, my daughter's boyfriend did some welding on the car's chassis (for it MOT). While they had the car, boyfriend said that everytime he connected the battery the alarm sounded. So, together they reset the immobilizer using the EKA code and rotating the key in the barrel. I've questioned them till I'm exhausted, but it is like pulling teeth trying to get some detail. When I got the car back - problems, as described in my original post.
I am thinking that now I am faced with either replacing the RF receiver or buying a second key. Since I live in a rural area with very little crime, might it be easier to just bypass the immobilizer. I've looked on this website, but can't find anything specific for how to do this on a D2 TD5. Can someone advise on how to do this or direct me to a relevant post please?
Thank you for all the help.
As what you are asking is basically "How can I nick a Disco once I've got the door open?" you won't find it I doubt.
But someone may be willing to PM you with the info.
 
might it be easier to just bypass the immobilizer.

You can't "bypass" the immobiliser all you can do is to disable it with nanocom or hawkeye once the vehicle is remobilised, while it's immobilised you can't do anything
I am thinking that now I am faced with either replacing the RF receiver or buying a second key.
You have to rule out the receiver first cos if that's the problem a second key is useless
immediately before this problem occurred, my daughter's boyfriend did some welding on the car's chassis (for it MOT).
if the battery ws not disconnected before the welding the BCU can have issues now.
 

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