Imperialism 1 runs fine on my W10 laptop. Unfortunately I can't get any in-game music. Only the ambient sounds.

Anyone has any clue on why?

Hello !! I have nearly the same issue: game starts with music. But after one round of gameplay, there is suddenly no music anymore. Only the unit and industry sounds (ambient sounds) are still playing. Any new ideas how this can be fixed ?? The hint with renaming the winmm.dll-file (from other forum posts) does not solve the issue. There are already several topics in the forum, with the music issue. Help by the GOG team would be appreciated, as this seems a common issue for Imperalism 1. Cheers !!

Unfortunately, none that I know of.
Which is a shame, considering that Imp2 works perfectly fine, without any issues whatsoever.

I started up IMP1 to check.
I had no music either but I don't know whether I chose that setting in de past or whether it's the default.
On the opening screen, there's quill & ink pot. Clicking it gets you into the preferences screen where you can change the music volume.

You mean that you manage to hear music during gameplay now?

yes
you can also change the settings from the gameplay window

Thank you for your help.
But, unfortunately the problem does persist. When you first start the game it does indeed play music as it's meant to be.
But - after you finish a battle and return to the man map - all the music stops. And it doesn't start playing again. Even if one saves, quits the game and later loads the save, there's still no music. It must be some sort of bug in the game's code which is preventing the playback. Which, for some reason, is triggered by the battle events. :(

Thank you for looking into it, anyway.

I hadn't tested with battles. Too bad about that.
When IMP1 was first released I turned off the music so I could listen to my own CD's so I never ran into this back then.