This problem has been solved, but just for future reference:
We were unable to receive incoming calls on our landline, but we had a dial tone and could make outgoing calls just fine. Everyone who called us got a busy signal, even though the line wasn't in use. When we called Verizon for technical support, they re-booted our router, checked our lines remotely, and had us disconnect our phones (in case the actual phones were the issue), and nothing worked.
It turned out that somehow "Do Not Disturb" was activated by pressing *78. We were told to press *78 again, and it fixed the problem. Of course, we don't know how the "Do Not Disturb" was activated in the first place, since we never use it.
