THANK YOU SO MUCH FOR THIS!!! I have no practical soldering skills (other than inadvertently burning myself, which I of course did while making this repair), but this was easy to follow along. I paired it with a replacement of the original woofer, since the foam surround had deteriorated so badly it was unusable, and it seemed easier to replace than re-foam.
I'll just note that on my unit, the wire that was GREEN in your example was BLACK in my cabinet. After the repairs, I closed it up, and it worked perfectly. Now the subwoofer is too loud for my tiny apartment, but that's my neighbor's problem!
REINSERTING THIS CABLE WAS ABSOLUTELY THE MOST DIFFICULT STEP IN THIS WHOLE PROCESS!
Key points:
•Make sure that it's inserted evenly. It's tempting to get one edge in, and then the other, but that approach will prevent it from seating properly.
•The cable goes all the way in. There is maybe 1/16" of the little grooves showing, but not much more.
•Once the cable is properly seated, use a piece of tape to pull it all the way in, and keep the tension on the tape as you use a sprudger to flip down the retaining flap.
•It's a fragile connection, and if you break the cable it's a top-case or keyboard replacement, which is either expensive or a PITA, so patience is key.
I found it easiest to grab the connector where the hinged metal piece connected to the body.
Replacing this connector was a bit fiddly, as you have to make sure it's lined up exactly before pushing it in, and because pushing it in requires a bit of force.