HANGOUTS settings will override SMS Messaging settings. My daughters new (Verizon) Galaxy S4 Mini would only count one incoming SMS text after a reboot on the Home screen, while 2+ unread text messages were waiting within the SMS app.
Go into Hangouts> Settings and deselect the checkbox that redirects SMS messages to Hangouts. Be sure to go into the SMS>Settings and enable Notifications. This solved the problem for us.
Best of luck:)