My immediate thought when seeing this thread was Marble Madness (Arcade), which surprise surprise is also from 1984. It was a good year, eh? I think the musical complexity is way ahead of its time. This video has a bunch of songs. (Note that the uploader has added some additional reverb.)
http://www.youtube.com/watch?v=PkSffHjSyTY
That Paper Boy tune is ace though
same composer isn't it (Hal Canon)?