Get your heads round this electrics

Hi all have this 2001 discovery 2 td5 the key fob will not open the door have changed battery and had hawkeye on to the system and doesnot see the key,
also when you drive the immobiliser light , trailer and seatbelt light come on then go out if the fogs are on they go out with them, this about every mile.
also the radio and cd all work but with no sound then you get a blast of sound then off this can be at any time.
any help to get my brain back

Check for water ingress/corrosion at the BCU plugs and also at the IDM. Here is an extract from RAVE(workshop manual), to see that there is a problem with one of these(or a wiring/communication issue with the involved parts)...if uhave RAVE see the whole section about BCU cos imo that's your problem

General
The Body Control Unit (BCU) is located behind the passenger glovebox and is connected to the main harness by four connectors on its bottom edge and an additional connector located on the side of the BCU casing. Mounting the BCU behind the fascia makes it reasonably inaccessible for intruders to disable the anti-theft system.
The BCU uses solid-state microprocessor control to perform logical operations and timing functions for a variety of the vehicle's electrically operated systems, these include:
l Door locking.
l Anti-theft alarm and immobilisation system.
l Exterior lighting including direction indicators and hazard warning lamps.
l Courtesy lighting.
l Wipers and washers.
l Electric windows and sunroof.
l Heated windows.
The BCU also communicates with several other electronically controlled systems such as the EAT ECU and SLABS ECU and also has a datalink between the Intelligent Driver Module (IDM) and the instrument pack. The datalink is a low speed bus capable of transmitting and receiving messages at a data rate of 10,400 bits per second. Additional inputs and outputs to peripheral devices are included which are necessary for determining vehicle status for particular logical operations e.g. crank, ignition key inserted, fuel flap enable etc.
The BCU receives its power supply from the engine compartment fuse box, and is protected by a 10 A fuse. The BCU communicates with the IDM to provide the control signals to perform power switching operations in conjunction with dedicated relays.

IDM
The IDM is integrated into the passenger compartment fuse box, which is mounted behind the fascia below the steering column. There are no harnesses between the fuse box and the IDM. The IDM performs the power switching operations for several of the vehicle's electrical systems.
The IDM communicates with the BCU and the instrument pack via a serial interface. If the BCU or the IDM is replaced, the communications link between the two units has to be re-established. This can be done either by switching on the ignition and leaving it on for five minutes, or by using TestBook. The vehicle immobilisation will remain active until the
communications link between the BCU and IDM has been re-established.

Thanks for that will give it all a look