The immobiliser itself is a Clifford of some stripe -- it's quite elderly, as it was fitted when I bought the car ten years ago. It uses little black keys with a 3mm (or so) plug coming out of them, which you insert into a box which is fitted to the bottom of the dashboard. There's a flashing red light to show that the immobiliser is active; when you insert and remove a recognised key, the light goes off and you can then start the car. Except, of course, when it has forgotten that (either of) your key(s) are recognised, when the light _doesn't_ go off and the car remains resolutely unstartable.
Don't suppose anyone knows how to reset one of these beasts, do they? I have some vague recollection of doing something arcane with holding keys in for longer, inserting them multiple times or something of that nature, but any manual that came with it has long since gone the way of the dodo, and the Clifford website seems not to have anything relevant on it. (Not knowing the product name is not helping, but all of their modern stuff seems to involve either keypads in the car or remote controls on key-fobs, neither of which I have.)