Water is seeping along the entire north wall of our basement, which just happens to be where the boxes were stacked (the Rubbermaid bins were against an internal wall). The bottom row of boxes is soggy and moldy but the contents seemed to have come through ok, except for some books. I had to pull out all the contents and repack them and pull all the boxes away from the wall. Right now, the basement looks like a maze of boxes and I'm still waiting for the caretaker to bring over his solution- a box fan. Thankfully we are moving out because I don't want to live here in the damp, moldy environment any longer.
Here's a picture of what I found today: