(Marmaduke, my quote says quite clearly that not all Disco 1s have a spider but it does say that all from 1996 to 1998 DO have one. It is buried under and behind the radio mounting position, nothing to do with a green box in the passenger side footwell.)
So Tbag, as yours is an autobox it will have an EDC and therefore, as you said appeared, it is likely to have a check engine light, or something that looks like it. My research seems to indicate that it is inside the rev counter at the bottom centre, but this is only from research on the internet. The Diagnostic plug, which is NOT OBD11 compliant, is to be found top left in the driver's footwell. You will need Nanocom, Hawkeye or Scantool, or you need to get this truck to a proper Land Rover garage or a Land Rover specialist. I know it is a pain, but before I got a Scantool I once had to get my D2 to a garage and it involved my other Land Rover, a mate with a trailer, another mate with a winch, just for 15 minutes simple work with a diagnostic tool. Since then the Land Rover has worked fine. Anything to do with ECUs is a pain unless you have the proper kit and know what you are doing. I have the scars to prove it. BUT a decent diagnostic at least points you in the right direction and stops you spending money on bits in the hope one of them will sort the problem out. In the end it is cheaper than a new battery for instance.
If your dad never used the fob, it must mean he never locked the car, so maybe the battery in the fob is flat. There is such a thing as an EKA, emergency key access, and the number was given to the first owner of the vehicle. If you don't have it, a main dealer will give it to you provided you can prove you really do own the vehicle. I had to show V5 and another form of ID to get this for another vehicle. Once you have it you can get into the vehicle without setting the alarm off as soon as you try to turn the key. But it is termporary and will go back to needing the fob eventually, e.g. if you disconnect the battery. I do hope you manage to make some progress with this and if you are still stuck keep on posting, we will keep trying to help you.