You may be unable to sign in to a Google account on your phone.
Ensure first that you have a data connection and that it is working by opening a few webpages in your browser. If your data connection is not working, see My browser shows a "No network connection" error.
After confirming your data connection, from either a computer or your phone, navigate to http://www.gmail.com and sign in. If you get an invalid username error, but the username is correct, one of these actions may resolve the issue:
If you changed the Google password, access the Play Store to sign in. If it does not prompt for a password, then follow these steps to clear the cache for the Gmail app: