There is essentially no difference, unless the context makes it so. For example, have you had a car before? might imply that you now have your FIRST car. While, did you have a car before? might be the question if the person NOW has a bicycle.

Well for me, the first one would be best written "Have you ever had a car before?" The present progressive includes an unspecified past up to this moment, in other words at any point in time before now. The second one seems to be missing some information. "Did you have a car before... what?" Because the simple past refers to a specific to a time in the past, I am looking for some information after "before". Before what? The crash? The flood? Did you have a car before you were 21 years old? Does that help explain things?