Did you buy this phone second-hand(used)? If so it may be the case that the previous owner set up Activation Lock. That would kick in when you restored it and give a message including a partial Apple ID which is not your own.
If this is the case then only the previous owner can unlock it, either by providing you with the account ID and password, or by removing it from his list of devices (as he should have done before selling it) - please see http://support.apple.com/kb/ts4515
If you are unable to contact him to do this then I'm afraid you will not be able to use the device - there is no other way of unlocking it at all. Apple cannot unlock it for you.
You should if possible return it to wherever you bought it and ask for a refund as in this event the device is completely useless.