Humm...I'm not playing SH3+GWX at the moment, but looking in my notes and files I see that I have added a personal mod just to make the music play in the game...so hey, I cannot really have sound problems
BUT: that could also mean that by default there is NO music in-game with GWX, and so no music in the menu. You can check that by going in the data\Sound folder. It should contain 5 folders, with a total of 19.480 sound files. My mod has added 35 music files in the music folder for a total of 42 files.
Have you applied the 4GB patch for SH3? Also you need to start the game in Admin mode, you can set the shortcut accordingly.
The GWX package consists of a behemoth manual of 500+ pages and I urge you to read the special section about configuration and specific error solving, there is an entire chapter for that.