Diagnosis
You're likely getting a picture signal from one of the HDMI ports, but the TV's main board isn't initializing the display driver correctly. It's a common handshake issue with this series.
How to Fix It
Unplug the TV from the wall for a full two minutes. While it's unplugged, press and hold the physical power button on the back of the TV for 30 seconds. This drains any residual power. Plug it back in and turn it on using the remote. If that brings the picture back, go into the TV's Admin & Reset menu and perform a 'Soft Power Cycle'.
If That Didn't Work
Try booting the TV with no HDMI cables connected at all. If you get the Vizio logo or smartcast home screen, then one of your connected devices is causing the conflict. Reconnect them one by one to find the culprit.
Heads Up
If the black screen happens repeatedly, it can sometimes be triggered by a specific HDMI-CEC setting. Try turning off CEC (called 'System Standby Control' in the Vizio menu) on the TV and see if the problem stops.