If you want to use the ogg-winmm wrapper you need to rip the music tracks from the CD into .ogg files and put them in a "music" folder. Have you done this?
Also there are multiple forks of ogg-winmm some of which can not play the music in HeavyGear. My fork should work with the game:
Personally I prefer to use Dxwnd to play HeavyGear1 since it supports the 1.2 patch and runs nicely with FPS limit using Software or Direct3D rendering.
If you want to try Dxwnd you can get it here:
(click on the green download button)
Then follow these steps:
0. Make sure you have a clean HeavyGear setup with no other wrappers in the game folder. Patch the game to 1.2 if you want to.
1. Extract Dxwnd into some folder of your liking. Do not put it in the game folder.
2. Run Dxwnd and from the menu choose "File" -> "Import...". Navigate to the Dxwnd\exports\ folder and select "Heavy Gear.dxw".
3. Right click on the new "Heavy Gear" entry and edit the "Path" to match where you have HG.EXE
By default the game is configured to run in a 800x600 window but you can select for example "Desktop work area" and "Keep aspect ratio" to get a larger picture.
4. You should now be able to run the game through Dxwnd by double clicking on the Heavy Gear entry.
Note that Dxwnd also includes a build-in cdaudio emulator which you can enable using the expert mode. Dxwnd is a quite complex piece of software but there are comprehensive help documentation which I recommend to study. There is also a discussion board at SourceForge where you can ask for more help.