how's the socket look. I know my cigarette lighter itself was badly corroded. The socket wasn't in to bad of shape so all I needed to do was replace the button part. Have you pulled the panel out to check if it's even plugged in. Someone may have worked on it over the years and not plugged it back in.
many years ago mine stopped working, there are a couple washers in the socket that transfer the the electricity 12v to heat to the coild.. one is like a fibre and the other metal. I replaced those with some old parts of stuff I had... and it has worked fine ever since..
if you can't figure that out, probably go to a a junk yard and find the parts..