What causes a 1988 Lincoln Town Car to start and run for a while but when you turn it off it just cranks and will not start?

I'm not totally sure because I have to see it and take a look but it sounds like your starter is going bad. Either that or I would say that it is the solenoid switch gone bad. If this doesn't answer your question please go into better detail because I would like to help you figure tha problem out. :-)