So this started happening to me this morning. Some Google searches showed a handful of others with this weird half screen issue (same side for the few photos I saw). After some troubleshooting with Google live chat, I'm getting a replacement unit. It should be new since they had me order it, but they will refund that charge once the RMA is received.
FWIW, I was also experiencing the random reboots others have posted about starting after the May security patch, so hopefully this new unit is free of all hardware problems.