I had the same issue with the Logitech z623 subwoofer not working immediately after purchase and setup.
What I discovered was that the issue was having the correct setting in your Realtek Audio HD Manager software. You would think that the right setting is to select a 5.1 speaker configuration and then uncheck the center, side and rear speakers so that only the front left and right and subwoofer remain selected. You would think that. I did. And that was wrong.
Apparently these speakers and many others nowadays can separate the subwoofer frequencies on their own. So leave the Realtek set to a 2.0 front left and right configuration. That way it sends all the sound through the one connection that you use to connect your subwoofer to your computer sound card. The subwoofer supplies power and passes along the correct part of the audio to the speakers which connect back to it, and the subwoofer finally works!