The capacitor that drops the mains voltage from 230VAC to 25VAC has dried out and is no longer regulating to 25VAC it is a lot lower.. thus there is not enough voltage to operate the relay. This is why tapping the relay or slamming the fridge door makes it suddenly work. it will only work till such time as the temperature is low when it switches off , when the temp rises again you are back in the slamming door phase.
The part you need is about 59p ... 33uF capacitor. If you are no good at soldering or general elastic trickery , then you can but the board from ukwhitegoods.co.uk for £50 the part number on their site is 546039402
o0timbo0o, September 2010