The logic line is the main power line for the controller. You need 3 wires to get your controller working properly: data, 3.4V and ground. It's explained here: http://forums.modretro.com/viewtopic.php?f=36&t=7717
Yes, I had the same issue. Without a disc drive (or a WASP) the GC would normally show an error, but that doesn't happen in the system language selection menu and the gamecube just freeze