Disco 2 Alarm and radio

Evening,
Hope someone can offer some help, it seems bizarre to me but....

A week or so ago the alarm sounded for no reason I can see but when I went to turn it off the radio was playing. Because the car hadn't been used for a couple of weeks I thought the battery could be down so I put a smart charger on it for 24 hours and all was well until today.
Today I was on the road early and because the bulb in the clock is blown I used the radio for time checks. Now I never used the radio at all but for the rest of today the radio has turned itself on several times. Once it didn't respond to the steering wheel controls or the buttons. I've been thinking it's just dampness which this car has plenty of.
I didn't want the thing playing all night so I pulled fuse 16 and made sure there was no power to the radio which seemed to be the case but just before dinner this evening the alarm went off again and when I got to it the radio was playing without fuse 16 !
It's now parked up without the battery connected.
So if anyone has an idea if it's due to dampness or to a short I would be most grateful of any thoughts that could help sort it out.

Thank you.
Graham

Seems like water ingress/corrosion in the fusebox/IDM, quite common, the easyest way to rue it out is to find a suitable fusebox(based on MY) and swap it

Thank you Frey for your advice. So just to be clear for my car I will need a 2000 ES V8 one. Are there any other things I need to know about buying a second one ?
Thanks again.

There are 3 types: pre-facelift(what you need), facelift and late(2004) facelift so make sure that in the description of the item is stated that it's removed from an up to 2002(non facelift) modell and if it was a Td5 no problem just that you'll have to put a relay at the bottom slot if it's missing cos that's the ignition relay used only on V8s.

for example this one is good https://www.ebay.co.uk/itm/Land-Rover-Discovery-2-TD5-V8-Interior-Fusebox-YQE103320/254033491903?fits=Car+Make:Land+Rover|Modeliscovery&epid=645389669&hash=item3b259377bf:g:97MAAOSwsrlcG6Br , or this(which has the relay too) https://www.ebay.co.uk/itm/Land-Rover-Discovery-2-TD5-V8-Interior-Fusebox-YQE103830/254033492273?fits=Car+Make:Land+Rover|Modeliscovery&epid=650707009&hash=item3b25937931:g:BQIAAOSwzTFcG6CG

all you have to do is to disconnect the battery first then after the swap and reconnection turn ignition on II and let it so 5 minutes as the IDM and BCU to regain digital data communication only then try to start it.