The display being dim when cold is a common problem. Without replacing it (and there's probably no part available) I dont think there's any solution.
The interior lights and locking mechanism and detection systems are all controlled through a single "Central Locking Alarm System and and Interior Lights Control Module" in the boot on the left side near the wheel well.
The boot lid alarm switch is in the latch mechanism and feeds into this module.
Finding the Module would be a good starter for ten here. As well as getting VCDS scan 
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2002 D2 S8 – Ming Blue, Valcona leather, Vavona wood insert, solar sunroof (to be fitted), Heated rear seats, extended leather pack, 18” Avus, ski hatch, Bose, auto dim rear view mirror, rear blind.
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