When I was first trying to figure out what was wrong, I checked the camera power outputs with the meter while the cameras were still connected -- and got the 6vdc reading. I then disconnected all the cameras, pulled the box from where it was mounted, put it on the bench and checked the outputs again. Still 6vdc. That's when I submitted the post asking for help.
Then, of course, when I went to actually try billy's suggestion to troubleshoot it, the thing was working fine again.
In the meantime I had already ordered a new power supply box, since I had to get my system up and running again ASAP.
At this point my position on this whole situation is going to be, "You can never have enough CCTV power supply boxes, right?"