I received a Raspberry Pi 3 today and made a 64 GB µSD card with the latest version of Raspbian Jessie (with Pixel). I plugged in an HDMI <> VGA adapter, then the 2.5 A-rated power supply, and it turned on. I played a few minutes with the Pi, which was working really great, then I stopped it at lunch time by pressing the "Shutdown" item in the Raspbian's menu.
The green light doesn't blink after shutdown, just the red light. But when I unplug the power supply and plug it back, the green light blinks randomly and the screen doesn't display anything (really nothing, not even a line of text or a colored square).
I formatted my SD card and wrote Raspbian Jessie to it: that worked fine and I was able to boot up my Pi. After I shut it down, no boot is possible again.
Do you have any idea of what happened or how to fix ?