The なる was throwing me off a bit, but I think it’s necessary because the previous sentence is やがてドアは、音を立てるのをやめた. So basically, before long the door stopped making a sound. So the following sentence (the one mainly being discussed) is saying: (it became that) not a single コトリという音 could be heard from the other side of the partition screen.
I think I got it now.