If the HP hard drive diagnostics don't work and you get the boot device not found error, then it's most likely that your hard drive has died.
I would first suggest slaving the hard drive to another PC to see if you can recover the data off the old hard drive (not likely, but worth a try to see).
Then, you have several options.
First is attempting to run another hard drive diagnostic to verify that the HDD is dead/dying.
While it's slaved to another PC, you can run the Seagate Seatools for Windows (or the Western Digital Data Lifeguard) to test the drive
Both are free from the manufacturers, just search Google for them.
Then, if it is indeed the hard drive, you'll need a new hard drive and a copy of the HP recovery disk.
If you don't have the recovery disk (and if the system was W10), you can download one from here: https://www.microsoft.com/en-us/software-download/windows10
Select the "Create Windows 10 Installation Media" link.
This won't have the additional HP provided programs, so you may still have to visit the HP support website to download them.
If it's not he hard drive, then you have to wonder what's causing it - hardware or software?
The easiest thing to do is to try to install Windows 10 from the HP recovery media.
This will wipe everything off of the hard drive - so make sure that you have a backup!
If the Windows10 installation fails, then you'll have to assume that it's some other piece of hardware.
At that point, I'd suggest posting over in the Internal Hardware forums for more expert hardware advice: http://www.bleepingcomputer.com/forums/f/7/internal-hardware/