This is how I understand it. It may be right/wrong or bits missing!
Alarm/Central Locking : When you press the button on the fob to lock the car, it sends out a coded IR message/signal. This is picked up by the IR antenna inside the binnacle on the dash and the message/codes received by the CCU (there may be something between antenna and CCU to read the IR signals and relay them to the CCU). The CCU validates the code is for one of the fobs it has codes stored for - if it is, it then locks the doors and turns on the alarm. The same sort of thing happens when you press the unlock button. This is obviously working OK as the alarm and locking is working correctly on demand of the fobs buttons. The fact your alarm is going off will be due to one of the car's security sensors being triggered - these could be door/bonnet open switches,movement sensor etc. I'm not sure if the reason can be picked up by a code reader.
Immobiliser : When you start the car there are 2 computers at play regarding imobilisation performing different tasks. When the car is imobilised, the CCU does not provide an earth to the starter relay so the engine will not turn over and the engine's ECU will not fire the injectors. The imobilisation must turned off for these functions to operate. This is done as you put the key in the ignition, there is a 'coil' around the ignition barrel. When the key is inserted into the barrel, this induces a current that tells another part of the fob (key) to send another coded message - I'm not sure if this is picked up by the coil or the same IR antenna as the alarm. This is checked by the CCU and if valid it will then exchange coded messages with the engine's ECU. If both these codes are correct, then they both turn off immobilisation and when you turn the key the engine will turn over and the injectors will function thus starting the engine (assuming nothing else is broke!). When you turn the engine off, I'm not sure at what point it becomes immobilised again - it may be immediately, when you remove the key, a set time after or when the alarm is armed.
If you try and start the car and it is imobilised - that LED will light solid. I've experienced this at 2 different times on my Freelander; when the fob battery was getting low it would randomly light (and engine not turn over/start) obviously getting more regular as the battery drained, and the other time was when my starter motor was failing and it sent spikes of power through the car's electrics and screwed the CCU up - I disconnected the (car's main) battery for a while and reconnected it to clear this (as well as replacing the starter motor!).
I'm trying to be helpful,the the extent of my limited knowledge, but I don't think anything here really helps you with the diagnosis of why your engine won't start!
The above is a description of functions, and you would be advised to read up in the LR Rave workshop manual about them for more accurate info, there's info on how to download it here...
https://www.landyzone.co.uk/land-rover/rave-disk-maintenance-manual.260227/
These functions are different in different countries - for example cars sold in Japan had the imobilisation disabled. I'm also pretty sure I've heard scenarios where only 1 bit was imobilised - eg the engine's ECU and not the CCU - this would seem not possible, but I'm sure I have seen it reported. It would be interesting in diagnosis of the engine's ECU if there is an 'imobilised' bit and whether that bit was set when the dealer's ran their diagnosis test on it.
Really unless that light is lit there isn't really evidence that it is imobilised and it is likely to be some other fault, eg low fuel pressure or crank/cam position sensor - however, you would have though that the dealer's diagnosis would have highlighted any problems. Having said that, I'm not sure I'd put much faith in a LR technician to be able to diagnose faults on a 2001 car - they probably haven't hooked up a 2001 car, or any Freelander, for months - they tend to just work with the higher paying newer (posher) cars - I know my local dealer has not been interested in F1's for years now.
You might find that an enthusiastic independent diagnostic specialist who can hook into TD4 Freelanders would give a better/more thorough job.
