Spectre laptop will not boot (or display is black) unless preceded by a hard reset

[tzackin]

I am trying to solve this problem for a friend.  Her laptop seemingly can only be booted after a hard reset.  It is possible that it is booting and that the display isn't working but I cannot unequivocally distinguish between the two.  I suspect it is the former though since, without the hard reset, I cannot even get into the BIOS.  I tried running the HP software to update the BIOS but the update option was disabled. I don't know if that is because the latest firmware is already installed or for some other reason.

I have run the BIOS diagnostics and I am running a more thorough version now but there don't seem to be any hardware issues.  I have updated the one video driver that was old.  I have updated Win 10 to the latest version available, but the problem persists.  BTW, it also seems, although I can't swear to this, that the system will not start up normally even after a hard reset if the power cable is plugged in.  I only mention this because I have seen other problems with other HP laptops related to the battery.

TIA.

[tzackin]

Update:

(1) The primary screen works when the system is cold. However, even when cold, if you try to restart immediately, the screen is black.
(2) The HDMI port works perfectly whether the machine is cold or hot. Other than the built-in display the laptop works perfectly on my TV.
(3) I have updated the video drivers for both the Intel and NVIDIA chips without success but, as I said, they work fine with my TV.
(4) Although I presumably have the latest firmware I have tried to update the BIOS yet, despite poor instructions, whatever changes were made, if any, made no difference.
(5) All diagnostics succeed for all componenets.

Bottom line:
(1) The laptop works fine.
(2) The screen, when it gets detected (which is rarely), also works fine. The touchscreen works whether the built-in monitor is detected or not.
(3) The video card might be flaky -- it sometimes forgets the appropriate resolution -- but seems to work fine with the HDMI port so I am reluctant to point the finger there.
(4) Since some others have been having the same or similar problem how come no one can come up with a fix for this? If it is hardware why is there no low-level diagnostic that can recognize the locus of the problem? It is unacceptable that such an expensive machine should have such problems after only 3 years of relatively light use. And, as much as I would love to have it fixed for a reasonable sum, I have no confidence that it is fixable since no one can point to an obvious culprit.

Question: What are the odds that replacing the motherboard would solve the problem? I see they are available on eBay for around $200 so a $300 repair might make sense. The only problem is what if that doesn't solve the problem.

Thanks to anyone who can provide an answer to this issue.