For the last few weeks I've regularly had an error message appearing on my desktop. It says " Username and password do not match. You provided (my gmail address). Please enter your full email address (including @domain.com)".
You should try to clear the saved passwords:
Under Firefox go to Options > Security > Saved password.
Clear the passwords.
You can also uncheck "Remember passwords for sites".
Sign-in to your Gmail account and if it is OK you can re-activate the "Remember passwords for sites" option.