You will most certainly need to update the file to a newer version of Director - and I would suggest using the latest version (11.5 currently). You'll probably have to pass it through 5, 7, (8.5?) and 10 before hitting 11.5, though you could try a direct update to 11.5 and see what needs fixing (or if it will even update the file). You will need a copy of the original source .dir to do this with.
I agree with Sean. Use the "update movie" function in all the aforementioned versions of Director and it'll work. Director 4 was released in 1994, during the good ol' ages of Win 3.1x and Mac OS 7, and it's easy to see why Mac OS X won't run your movie, as Classic Mode was abandoned when Apple stopped making PowerPC Macs. The only way it would work on Mac OS X without updating the movie to work on Director 11.5 would be if you were to install Mac OS 7.x in an emulator like BasiliskII or SheepShaver and run it from there. Some software made with Director 4, such as Total Distortion, WILL work on Windows XP, though, and probably all the way through Vista and 7, albeit only on 32-bit systems. This is because Director 4 for Windows was 16-bit, and 64-bit Windows can't run 16-bit applications.