As it sounds like you've figured out it has absolutely NOTHING to do with the CD pickup/laser lens assembly. It might be a dirty volume control. The first thing that I would try if it has a volume knob (as apposed to up/down buttons) is with the unit powered off I'd move the volume between the minimum and maximum settings several times quickly. It could be a number of other things too.

it is also about the same odds (50/50) of it being a multi-wire umbilical cable inside the unit that the volume signal happens to be carried on, or an associated solder connection/plug..

Yep, it could be lots of thing. Most not user serviceable. The reason that I mentioned the volume control is because it's one of the few things that anyone can try.