iphone 5s screen goes black and no restore possible

hello, the screen of my iphone 5s went black all at a sudden

I tried to restore it via iTunes, however at one point i get the request to enter the SIM code to unlock the phone - which is not possible since the screen remains black. The phone gives a periodical acoustic signal, eventually something to remind one to enter the PIN ?

after a second attemp of using the restore function in iTunes, I get now Error 3014 and when opening the terminal window and using the

"sudo nano /private/etc/hosts" command, I don't see an entry containing “gs.apple.com”, as the related article on the Apple Website here: http://support.apple.com/kb/TS4451 mentions to look for …

if someone here has a suggestion that would be brilliant

warm regards,