Most likely to do with malfunctioning Discrete Graphics Card.
I had a MacBookPro 15" Retina suffering from same problem only after 2 years of use.
Upon a power down or restart, the screen goes black. The keyboard is still responsive.
To get the screen back, it is possible to put the laptop into sleep mode. Make the unit is turn off first, then press the power button to start up. When you notice that the keyboard backlit is on, perform another short press the on/off button to put the unit into sleep mode, wait for about a minute, then press on/off or any key to bring the unit up. In most cases, this (for some reason) will activate the use of the built-in Intel Integrated graphics card.
You should be able to use the laptop for most application, limited by what performances the Intel Integration Graphics Card can offer.
In most cases, if you only put the laptop into sleep mode, the screen should come back on when awaken. However, if you put the unit into shutdown/restart mode, you will need to repeat the above process to get the screen to display.
This is only a workaround to get the screen working, it is not a fix.
As mentioned by other solution posted, the discrete graphics chip needs replacing, which can be a costly fix. However if integration graphics is all you need, this workaround may be an acceptable solution.