Get the multimeter out. Did you check if the cig lighter has power at the wires going into the back of it? That would be the first step. If it has power there, than something is wrong with the connections in the things itself. If it doesn't have power there, then there is something wrong with the wiring. So if that's the case, start either at the cig lighter and work your way back to the fuse box or start at the fuse box.
But get the multimeter and start checking stuff.