В /etc/init/gdm.conf добавьте строку
and net-device-up IFACE=eth0
для начала в операторе (замените eth0 на нужный вам интерфейс). Должно выглядеть
start on (filesystem and net-device-up IFACE=eth0 and started dbus and (graphics-device-added fb0 PRIMARY_DEVICE_FOR_DISPLAY=1 or drm-device-added card0 PRIMARY_DEVICE_FOR_DISPLAY=1 or stopped udevtrigger))