Hi Bigvee
Here's some background information which may help. The key has three things:
1.) Physical metal key blade to engage with ignition switch and door lock
2.) Battery powered remote control code transmitter that transmits up to (say) 50 metres to a receiver in the dash and operates the central locking.
3.) Induction (cordless) powered coded chip that transmits up to (say) 20 mm to a doughnut shaped receiver coil surrounding the ignition switch keyhole, and operates the immobiliser.
The three things are completely independent, so changing the remote locking battery won't affect the immobiliser.
If the vehicle part of the immobiliser can't recognise the code from the chip (or can't even get a coded response from it) the red padlock symbol will stay lit and the engine will turn over but will be prevented from firing up so there is no point in trying. The immobiliser chip is designed to work only over a very short distance, i.e. with the key in or very close to the ignition switch. Once the code is deemed OK and the engine is running it is not allowed to cut out, for obvious safety reasons. However, if things are erratic you could easily find that you start OK first thing in the morning, then switch off to refuel and find that you can't restart.
I'm not aware of any easy way of extracting the coded chip and its own miniature coil from the key fob in order to get it even closer to the receiver coil, but I guess nothing is impossible. As communicator mentions, I have a theory that the coded chip in the key and the vehicle receiver start life properly tuned to the same frequency, but after several years one or the other drifts slightly off tune and things start to become erratic.
Some people have reported that the receiver coil, or the two wires to it, goes faulty. So you could try a replacement if you are prepared to take a chance.
It may be worth trying the van key on its own, i.e. with no key ring or other keys nearby. It may be worth trying another key, if you have one.
As far as I know, the code of the chip in a factory supplied replacement key is fixed. So if you get a new key with a different code, the vehicle part needs to be reprogrammed by a dealer so that the new code is added to its "good" list.
To the best of my knowledge, UK Ducato X250's didn't come with a factory alarm. Some (especially motorhomes) may have had one dealer fitted. They normally have their own independent remote control fob.
If you encounter a DIY fitted alarm, this might also have immobilising features. It may be best to remove or at least bypass it whilst fault finding.
Sorry I can't offer more detailed help.