I mentioned the MP3 player or phone because I wanted you to try it with a different source than your laptop. This was to be a troubleshooting step.
However, since you reported it works fine with headphones, and you have the same issue with a different laptop, we can be pretty confident that it's not the laptop. If the laptop emits correct sound to headphones it will do so with anything else.
And since the speakers work fine without the subwoofer box in the path, it isn't the speakers.
The problem is almost certainly somewhere in the rest of the setup: The cable from the subwoofer to laptop; the jack on the sub box that the speakers' plug plugs into; that volume control dongle, or inside the subwoofer box itself.
Sorry about this, but I doubt there is anything you can do to fix it unless you have a little bit of electronics tech competency: soldering, identification of wires, etc. And depending on how complex the subwoofer box is, the problem might be on the actual amplifier board inside, in which case it'll need a lot more competency. A lot of repair shops won't even touch it, because no schematics or other troubleshooting aids are normally available for this stuff.
So: If it's in the "free return" period from wherever you bought it, do that. Otherwise, if it's under warranty, return it to Logitech for repair. Failing that, investigate local repair shops.
(Terminology nitpick: Note, plugs are the things with pointy bits, jacks are the things with holes. If you had a hole in your boat, you'd want to plug it, right? Plugs fill holes... It isn't an "aux" anything, either. "Auxiliary" connections are normally for devices other than "the ones the device already has specific labels for.")