First make sure that the cigarette plug is making good contact in the socket.  Try reinserting the plug a few times.

You can also check the fuse by unscrewing the tip of the cigarette plug.  There is a spring inside, be careful not to lose the spring.  The fuse size is 1 amp.  Replacement fuses can be found at Radio Shack.

If the problem persists, then please try a new power cord.