Typically when a mobile device is locked, it wants the original e-mail account name and password it was setup with. You shouldn't need internet connectivity to unlock the phone. If you can log into your account at https://mail.google.com/
that's good, but it doesn't guarantee it's the same account the device is using or the original password used.
In some cases, if the device can receive a call, you can access the menu during the call and disable the screen lock.
If you don't remember the username and the account was properly setup at creation time, you can recover the name using "I forgot my username" here: http://support.google.com/mail/bin/answer.py?hl=en&answer=46346
And here's a trick to recover an account name on an Android device: https://productforums.google.com/d/topic/gmail/ydNElvUjJVU/discussion
If you have the username, the following will help with the process to recover the account by resetting the password: http://gmailaccountrecovery.blogspot.com/
BUT... A recovered account or changed password won't have the original password which is what the device needs to be unlocked. In that case the device will probably need to have a factory reset done (read the owner's manual for instructions) and then setup again with an e-mail account (be sure to write the information down this time). If it's setup with the recovered e-mail account, any purchased apps and synced data should be restored. If a new account needs to be created, all previous information will be lost.
An article on this topic: http://einartysen.se/unlock-android-phone-after-too-many-pattern-attempts/