iPad Pro no display both on its own screen and external monitor

A few months ago my 12,9" 2015 iPad Pro suddenly has a black screen, if I press home or power, I could see the backlight turning on. Since the replacement screen is pretty expensive compared to its current value, I just left it at a table, untouched. Few weeks later, I accidentally pressed the home button and the screen worked as normal.

This functions normally until almost a month ago the screen suddenly went black again. No problem, I thought, just wait a week or two and it'll be fine again. But no, it's still black until now. Yesterday tried to connect to an external monitor with Apple's Lightning to HDMI adapter and it didn't show anything both on the external monitor and the iPad screen it self (iPad's screen backlight is turning on if I press home / power). And before you ask, I could use the HDMI adapter just fine with another iPad.

So what could be happening here? If it's just the iPad's display, I could see that maybe the screen or internal connector caused intermittent problem. But if there's also no image using HDMI then maybe it's not actually the screen itself that's causing the problem?