Ok, you're running original 1998 game discs? I think I know the "issue" now, though it's not really an issue. The 2012 Square Enix Store and 2013 Steam releases have the updated data\music_ogg folders with looping OGG music files. The original game had the .midi files in data\music. This isn't a problem for you, as you just need to download the Media - Music and Sound category from the Catalog and run one of the music mods there.
I may have to make a 2nd GC for anyone using the original game discs, and have it place the original music in the music\vgmstream folder. That's only needed if you want to play with music and without downloading the Media - Music and Sound category from the Catalog.
Does the opening movie with Aerith/Midgar play for you?