Well... I have Ubuntu server installed on one of my laptops with a gui (xorg
and gnome) and I can say at least that for basic internet function,
networking behaves the same on both. The server, just like the desktop
version, doesn't actually have any server "services" installed by default,
though there are options to install some services during the installation or
after, depending on preference. There's really no difference between the
"backbone" of either type of install. The only reall diference is that the
gui gives you the option to install via synaptic rather that apt-getting
everything. Granted, none of that info really helps you much with your
current issue.