Screen froze, battery charges, and lights come on, but no display

OK, so I was using the Samsung virtual keyboard in an app to chat when it glitched and froze the app. I couldn't close the app or backup or do anything, so hit the power button to lock screen and try and force it to unfreeze. it locked and.... nothing returned. Just a black screen. During my attempts to get the screen alive again it turns out I took some screenshots which uploaded to my cloud - they show the unlock pin page and power off/restart page, so I know it was still alive. The buttons at the bottom also light up when hitting the power or home buttons. However, forcing a restart did nothing. I waited for the battery to die and then tried to restart.... nothing comes up on screen. No battery charging screen. Once there's enough juice from a charge to power up the tablet I get no restart screen. But the lights at the bottom come on. I plug into my PC, yes it sees the device (once I've charged it a little).

So the battery works fine, the charging works fine. The screen does not appear to. I simply CANNOT access the reboot screen! Can anyone help please?