Okay, I went by my church late this morning, and looked at a few things. First, I tried testing the lines. My cable tester showed no problems there. Next I tried attaching a new switch to both ends of the lines, and had the same problems. Lastly, I tried poking what I thought was cement, and while I don't have experience with the substance Mark mentioned, I'll eat my hat if this stuff isn't cement.

I've created an album of photos and videos to demonstrate. I have a photo of my cable tester, a video of a test, and photos and a video of what I assume is cement.