I faced this error last year when we tried to move to EasyEngine, but unable due to this error, now having again. Message we are getting
Error on Functon *table_name* - Access denied for user 'www-data'@'localhost' (using password: NO)
Things we have tried
Give all permission to the DB User created by EE
Create a new user
Disable the plugin that use that specific table. Then it hangs in the next table
Tried to connect to our remote db server from EE install, same issue.
So, its not a permission issue.
Basic WordPress install works fine.
We tried clean cookie, change timezone, update.
Site is on Latest WordPress 4.2.3 and we are testing on EE 3.3.3. And its almost basic EE setup with w3tc.