The key to how we knew the fallen ice hadn't woken us up lay in the effects of time. Ice keeps things cold by transferring its cold to them: the chilled objects, in turn, transfer their warmth to the ice as the system works towards equilibrium. As a result, a sort of footprint of the objects being chilled is slowly melted into the ice. The ice in our icebox had been laying against some jars of food and the side of the ice compartment long enough to melt into the shape of the things it was contacting. This is a natural process which takes several hours, so we knew that the fall of the ice couldn't have caused the noise that woke us up just a few minutes previously!
Have fun sharing this with your friends who like puzzles, and / or any chemistry or physics teachers you might know!