Yes, I think they wanted to return one more time but didn't have much time, or maybe they were hindered.
Well - that really sucks; most of us have "been there, done that", and to have someone break into your house is a real crappy thing to go thru; my sympathies.
I'm sorry I can't offer much in the way of "how to fix" your speakers - my first instinct, too, would be to seek a replacement (insurance or parts from Logitech). You seem to indicate that you didn't have insurance? Perhaps now is the time to consider it for the future. In the meantime, if you haven't contacted Logitech, do so by phone; you might be surprised by what you can accomplish via the phone vs an email. If you have done this (or do pursue it) and have gotten nowhere...
Ask yourself - is my time and effort attempting to fix this device worth it, or would it be cheaper to purchase something else new (or perhaps used)?
$80.00 isn't cheap for a pair of speakers and subwoofer, but if they meant a lot to you (or they sounded really good), and you have the time and experience - you might try recreating the control box and connections. I don't know how many pins are on that main connector at the back of the sub, but first count those (plus the shield as "ground"). Did the wires plug into the satellite speakers, or were they direct wired?
What parts of the system do you have left? If you have everything but the wires and the control box, then (in theory), you could probably come up with another controller - but its going to take some work. Something else - do you remember if the control knob was a "clicky" feeling thing that spun "forever" or an actual potentiometer knob? Also - a look inside the subwoofer at the amp might tell you some things about which pins on the main connector did what...
Ultimately, you might find it cheaper to purchase something else...