The most common reason for an oil filled radiator not working is that it has been covered by an item such as a towel or piece of clothing which then raises the temperature within the radiator which then blows the thermal fuse / cutout. These are normally found connected inside the radiator where the electrics are located and more specifically on the live wire between the incoming flex cable and the main switch. They look like a resistor and are normally covered in heat proof sleeving. If you do attempt to do this simple repair just remember a few things : make sure the radiator is unplugged before and during the repair, replace the cutout with one of identical value rating (take to maplin for advice) and finally make sure the repair is of a good safe standard.
p.s. the cutout should cost less than a £1.
....and remember if you are unsure either dispose of the faulty item and buy a new one or get it fixed by a pro.
Paul
April 2012