Try starting it up in "Safe Mode" and see if the screen shows or not. If it does, you have a bad app, malware, virus, etc., on the device you need to remove before it will work correctly.
If, however, it won't even show in "Safe Mode" then it may need to have the display replaced, if not something more serious. In that case, if it is under warranty still, contact the manufacturer. If not under warranty, then you can try a local tech.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.