In the days prior to a certain search-engine's rise to fame, thereby distorting the original meaning, the term "google-eyed" referred to a certain odd and slightly humorous appearance or expression in someone's eyes. Whether the person was slightly cross-eyed, cockeyed, or had a lazy eye, or simply postured their eyes in an odd way during an expression, they were "google-eyed."
In newer post-google.com use, it probably refers to someone who has spent far too many hours "googling" or web-searching for something and reading too many webpages.
A feeling of lostness and sadness that occurs during times of freedom on the internet when the world's most powerful search engine is before you, but you do not have the incentive or motivation or curiosity to look up anything interesting.
"I sat in front of the screen for about 10 minutes, completely google-eyed"