Used to have storage heaters myself, and the most common problem was the thermal overload link used to melt. Take the top off the heater, the link is normally about the size of a fuse you get in a plug. It'll be screwed on to the thermostat thingy. Might have a problem finding a replacement, usually try small electrical shops. Could try the net for Dimplex spares
If it's not the link then the element might be broken. This is probably not worth fixing. Try and get a secondhand heater out of yellow pages etc, and two strong men to lift it!