I'm playing Colonization II in windowed mode, on a 2-monitor setup: colonization in one monitor, web browser in the other.

but, whenever I click out of the Colonization window, or minimize it, I stop hearing the soundtrack.

in other threads, people have mentioned it going either way: some people hear background music when minimized, others don't.

Does anyone know what makes the difference, or how to configure things so that I do hear background music when minimized?

I think it's a case of what else you're doing. If you're doing something else that grabs the sound drivers it should cut out Col. Sometimes I get music, sometimes I don't. For me it seems to be related to that fact.