I thought the CTEK indicator lights would show the circuit wasn't charging? Could be the battery is goosed and it's trying the recycle mode? Seem to recall that can take many hours to complete.

Failing that, and if the fuse looks ok, use the croc clips or eyelets that come with the CTEK for the battery connection for now.

That way you'll know the battery is being charged overnight, and tomorrow you can try the cig lighter - if it heats up, your socket must be ok. If it doesn't you have some investigating to do.