If the satellites work then the problem can be either the subwoofer speaker or the subwoofer amplifier. You would have to connect another speaker to the wires that connect the subwoofer amp to the old speaker to find out. I doubt you will get any parts from Logitech but you can try. Fixing speakers in that price range often costs as much as replacing them especially if you have to pay a tech.
Call Logitech and see if they can do anything. Sometimes companies offer deals to keep customers happy.