When I launch the world and open to lan, the world doesn't show up on the LAN parties' multiplayer list. We tried hosting it on every computer, but with the same result

Usually, openning to lan will have the world show up on the LAN computers' screens and be able to connect normally, and well, play until the LAN game is closed.

After updating to 1.6.2, 1.6.4 and up, we were no longer able to find each others' games, and in some cases we do, but still won't be able to connect.
The game displays "Connecting to server..." but never connects.

Steps to Reproduce:
1. Launch up a singleplayer world
2. Open to LAN
3. Try to join from another computer

The game will display "Connecting to Server..." and will not connect.