Furring strips visible THRU drywall... On the FINISHED side!
My personal bet is that the cinder block is wicking water, which is wicking through the furring into the drywall. That will absolutely cause the issues you're describing.

My bet is there's no vapor barrier. You said there was no insulation and in-wall insulation is typically faced with tar paper, which is typically your vapor barrier.

If you're looking to fix this there's no easy way around tearing it down. You can leave the furring up, but I would add something like 6mil plastic over it before applying new drywall. You might also want to add some waterproofing membrane to the cinder block, to minimize the wicking.