Unable to resolve is the error for no network, so this would be the problem.
Wifi needs the network applet to start automatically, therefore the gui. Lan cables on the other hand should work.
You could of course use terminal commands to start it.
To test the connection jut type "ping 188.8.131.52" for example.
Can you give us more details about what package you installed before? Loosing the whole gui is some serious shit that should not happen and therefore needs to be checked.
Well, so that's why i'm unable to download everything. Can i turn on wifi from terminal? Ping does not reach the host, so connection is actually down.
By the way, i've installed 2 versions of python and this caused some troubles with dependencies when removed.
I just typed autoremove to delete all "useless" dependancies but seems that it actually deleted more of them. Of course it's my bad that did not read carefully the list of all dependencies being removed .