My S3's screen turns on and shows previews of text messages.I know you don't like this answer but Android phones (and I don't expect the G3 to be any different) don't turn on the screen when you receive a text, etc. That is what the notification light is for - to let you know that something has come in and in fact you can program different colors for different kinds of notifications (SMS, Voice Mail, E-Mail, etc). If your screen turned on for every notification your battery would be gone in a couple of hours.