The two systems are separate in terms of the power supply. First I would check the 240v side. Check there is power to the 240v switch if it lights up it will have power. Then check the terminals which the element is connected to. If there is power to these ( check with a multimeter ) then it is most likely the element has burnt out and needs replacing. When you do replace it it's worth checking that the thermostat is working again this can be done with a multimeter as if it's not this could be the cause of the element burning out ie the element is on all the time. Obviously when checking the thermostat ensure you have the power switched off to avoid accidental shock. Regarding the 12v system I presume you are aware that this is only designed to keep the fridge cold whilst travelling and therefore only operates when hooked upto the car and the car engine is running. If it doesn't work uunder thse conditions you will need to check the 12v element in the first instance and that 12v is getting to the element. Hope this helps. Just be careful when working on 240v and I suggest taking photos of connections before disconecting any terminals so you know what goes where.
mal
July 2010