Firstly, can you get to behind/under the socket? There is a simple clip that holds the cable on and it may have come disconnected.
The internal contacts easily corrode - have a look inside and - if necessary - wrap a piece of wet and dry around the end of a pencil and clean the surfaces up until you can see bright metal. Blow it out (!) and then try again. Use a dielectric grease to stop recurrence, if this is the problem.