Hi,
I do assume that you have tried to log in with you Gmail account and password. Problem is that you need to connect to the Google server when logging in. If the phone was shut off when your internet connection was inactive, it won't be possible to log in, and since you can't unlock, you won't be able to activate your internet. The only other solution is have your phone unlocked by a Samsung service center, then you'll get a full reset (your data and settings will be gone though).
