The immobiliser is only controlled by the remote key, putting key in the ignition never did anything with the immobiliser. On the dash there is a light to show whether the immobiliser is on. This immobiliser has always been a pain as it comes on automatically after a short period. So if you stop to pick someone up, for example, and turn off the engine, after a few seconds, the immobiliser comes on and the only way to turn it off is to use the remote to lock the doors and then unlock them, which is stupid, but that's how its always worked.
The handbook does show how to synchronise the key after changing the batteries, though I can't remember what it said, it's something like; zap door, turn key in ignition, then zap door for a while, or some such thing..
This really is something that only a main dealer can sort - I have had similar problems with Rover and MG keys and have struggled because there is no longer any dealer support network. At the main dealer all they need to do is plug the car into the diagnostic unit and re-synchronise the key to the car's immobiliser. If the key/fob is defective they will be able to order a replacement - expensive but probably cheaper than buying another car . . .