Normally this can happen for several reasons:
If none of this works for you then you need to make an appointment at the Apple store and have them do this for you. You will need your codes because they ask for them when you bring in the phone.
What did you do with your iPhone before , there are 2 reasons why the iPhone was stuck on connect to iTunes scree .
One of them is Jailbreaking program, you were running the Jailbreaking program on your iPhone, but you failed ,
Another of them is Update program .
i was going to update my iPhone to the latest version and i failed , the result was that i can not access my iPhone, there was nothing that i can do with my iPhone, it was stuck on connect to iTunes screen.
I came up with the following solution :
1:Trying to reboot your iPhone (Simultaneously Press and hold Sleep/ wake and Home buttons)
2:Use third-party software to fix iPhone stuck on connect to iTunes screen (That's what i did before)