HP Startup Black Screen - Strange behaviour!

This morning my laptop stopped working. When loading what appears is just a black screen. Nothing more.
The last thing I did on my pc was watching a film and I didn't download or install anything.
I tried to make sure that the screen isn't broken by plugging it to a monitor, but it still showed no response.
Afterwards I tried to enter the BIOS. By pressing ESC during loading it gives me a startup menu with multiple choices:

• System information
• System Diagnostics
• Boot Device Options
• BIOS Setup
• System Recovery

First of all, since something is appearing, this means that the screen is working (and i guess also the graphics card should be working properly).
So I think it is because something happened with the OS (could be an update, not sure, I had Windows 10).
Coming back to the menu, this is what happens:

• System information: just gives me some info on the pc
• System Diagnostics: lets me check the memory (should work but takes 20min and not sure if I would understand the output) and hard disk (which doesn't work, because it says that the software for checking isn't installed)
• Boot Device Options: enables me to select different Boot options
• BIOS Setup: tried changing some options but didn't help
• System Recovery: when launched the screen becomes black again, and after 5min a screen with HP logo (and under the text "System Repair") appears, but goes away after 30s and the screen stays black again (end result: nothing seems to have happened).

I also tried to install Windows 10 again, by booting an USB I have, and when running the HP logo appears with a circle that is loading and after some seconds of loading everything remains black again.
Overall I think it is something that can be repaired (I think somehow by installing a new OS) since we can still access the BIOS and other options (that doesn't really work), but I'm not sure how, I tried almost everything.
Does someone has some ideas?

Thanks for the reply, I have tried to run the memory test, but it just says PASSED and nothing else (no log file or other).
I'm not sure what else I can try. Can someone help?

1) Find 3- 5 flash drives that you can format ( > or = 8 GB)
These are drives that you may want to keep for troubleshooting this and other computers:
a) Create a bootable windows 10 iso
Download Windows 10
b) HP PC Hardware Diagnostics 3-in-1 USB Key (version 3.9)
HP PC Hardware Diagnostics | HP® Official Site
c) Memtest86+ version 5.01
Memtest86+ - Advanced Memory Diagnostic Tool
or
d) Boot rescue
Windows 10 Recovery Tools - Bootable Rescue Disk - Windows 10 Forums
e) Create a bootable Ubuntu /Linux flash drive
Create a bootable USB stick on Windows | Ubuntu tutorials

2) Test the HP hardware with the HP UEFI diagnostic key
Power on the computer and repetitively click the F9 key
Select the external USB hard drive
Report the results into the thread (use a camera or smart phone camera as necessary to post results)
If there is any problem posting then use one drive or drop box or google share links

3) Insert the windows 10 iso into any USB port
4) Power on the computer and repetitively click the F9 key
5) Select external USB hard drive
6) It may take 5 - 10 minutes for the iso to load while viewing the Microsoft Windows icon
7) Select language, time, currency, and keyboard or click next
8) Click troubleshoot
9) Click system restore
Start with the oldest restore point and keep repeating until you complete the newest restore point.
If all restore points fail or if there are no restore points advance to the next step
10) Click startup repair
If startup repair fails advance to the next step

For all of the command prompt steps please use a camera or smart phone camera to take pictures and post images into the thread. If there are any problems posting images please use one drive, drop box, or google share links.
11) Click command prompt > Administrator X:\Windows\System32\cmd.exe > X:\Sources> type:
12) c:
13) dir
14) d:
15) dir
16) bcdedit /enum
17) bcdedit | find "osdevice"
18) diskpart
19) list disk
20) list volume
21) select disk 0
22) list partition
23) select partition 1
24) detail partition
25) select partition 2
26) detail partition
27) select partition 3
28) detail partition
29) select partition 4
30) detail partition
31) if there are any more partitions on disk 0 please continue in a similar fashion
32) select disk 1
33) list partition
34) exit
35) bootrec /fixmbr
36) bootrec /fixboot
37) bootrec /scanos
38) bootrec /rebuildbcd
39) chkdsk /r c:
40) reboot
The chkdsk command may take many hours and typically displays an ETA in the Windows RE

Please use a camera or smart phone camera to take pictures and post images into the thread. There are additinal steps based on the results to the above commands.

Are you sure it isn't this issue? HP Notebook PCs - Computer Starts but Screen Remains Blank (Windows 10,Â*8) | HP® Customer Support