What can cause an electric water heater to stop working?
A few things to check: 


First check the boiler - is it heating water? Does your hot water tank contain hot water? If not, it could be the heating element, a fuse or part of the heater circuit. 
If you have a timer controlling the boiler, check it is working- does the relay trigger as it should? 
If that is all working but you aren't getting hot water to your rooms, next check your zone valves to see whether they open and close correctly.
Can you hear your water pump? 
Have you tried bleeding your radiators? 
Do you have thermostats in the house? Check they are working- usually a click as they trigger at the set temperature.