Macbook Air stalls in start-up: Socket is not connected

Hi all

Into a bit of trouble here. Suddenly my Macbook Air would not start - when starting normally it stalls on the grey screen with Apple logo and spinning wheel. A "safe start" with command lines does the same with launch message "Socket is not connected" (twice)

Googleing the problem does not help me that much - I have not done anything about the setup neither system files nor passwords (single user).
Since I can not access anything on the mac, I cant run any disc/dianostics tools.
Absolutely nOOb with Mac, system-wise (thus cant remember production year, OS version etc etc)
This is the picture of the start-up from the safe start.

https://www.dropbox.com/s/aj4hxta42to1ty0/DSC_0199.JPG?dl=0

Any suggestions what to do - or what my problem might be??

Thanks a lot in advance!!

Solved!

I guess first lesson learned would be: get to know your basic Mac commands.
Second lesson would be: I still have no idea how Apple got the rumour if being user-friendly (said that as professional User Experience Designer). I actually have no idea of what happend - but i´m writing from my computer.

Ran the recovery command - as stated above.
While the tool or whatever was downloading/working - got an error message Apple.com/support 2003f - and the machine seemed to stop.
Restarted (actually typed the wrong command, cause I would try again) and a disc utility tool loaded with four possible actions among re-installing os-x
Chose to diagnose disc - and got an error, should be repaired
Repair failed and it said I should back up as much data as possible and format drive ect
Just because I could NOT figure out what and how to do that, I tried to diagnose again - again failed.
Repaired - and then it succeeded!!!!

And I have no idea what went right the second time - but restarted and here I am.

Thanks for the great help - guess I should have stumbled upon that command in my search, but didn´t.