For the case... if you are adding a fan, I would have the new fan blow into the case, and the existing fan blow out. Airflow is called that for a reason.. you need to create a "flow" that pulls or pushes out the hot air. Try it both ways as well, see which one works better.
Come to think of it, it will also depend on where you are mounting it in the car, and if the car has items that partially blow the airflow from the fans.
For the lcd... I have seen several instances where people have removed the speaker on the back and placed a fan in that area. Fan mounted to the outside, blowing air in though the vent holes that exist where the speaker was. Too lazy and tired to search for an example now, but there is some somewhere on this board =)