HP 8560w LCD fail (black) after reboot

[VikingOy]

My HP8560w  is in perfect condition, except for one issue:  If the screen is shut down (turned off) after a while during use, for any reason;  sleep timer, screen saver, reboot or just normal shutdown, it doesn't come on again unless I wait for a week or more before I try to turn it on.  But then, it works just fine, and I can work with it for hours on end without any problems. The screen remains on for as long as I'm working on it.  But If I turn it off, or let it go to sleep, it doesn't come back on unless I wait another week or so. 

However, reboot or forced sleep causes no LCD problems if its done immediately after a successful power on. The problem shows up only after 10-15 minutes of use.

The computer itself boots perfectly all the time even though the screen is black, no error messages, nothing. I know, because if I connect an external monitor - everything is just fine.  Even if I don't connect an external monitor, I can tell that it  is booting normally, by watching the HDD activity LED, and typing commands that I know by heart, including a proper shutdown command. 

So it seems neither the BIOS nor Windows 10 itself is aware that the LCD is black. There are n driver issues shown in Device Manager. This model has the NVIDIA Quadro 2000M GPU.
Using a bright flashlight, I cannot see any sign of graphics elements or text on the screen (as if it was only a backlight problem). Since POST is also black, this doesn't seem to be a Windows driver problem. BIOS is 68SVD F.63 dated 27.10.2016

Does anyone have any clue as to what could cause this behaviour?

To me - it seems as if an electrolytic capacitor required to switch or signal the 'on' state to the LCD needs to discharge between each session (and this discharge takes a loooong time - almost a week).
I tried to remove the battery and the RTC battery, but that makes no difference. It still takes about a week before it will fire up again.  HELP!