After checking the cables again, it was discovered that the cables attached to the patch panel in the back are rightly not connected to anything, because they're not attached to anything in the front patch panel either.
When mapping the front patch panel, I mixed up my mapping of the front and the back of the patch panel, and thought there was something seriously wrong. It turns out it was just me, and everything is hooked up correctly between the patch panels.
That being said, there may still be problems between the front patch panel and the ADCs, if the posted shower map is any indication, so we need to verify that those channels are good.