Install alongside Windows 8 is not working

First, try disabling Secure Boot, if you haven't done so already. This feature can sometimes cause this symptom. If that fails, be aware that HPs are known to have buggy EFIs that make dual-booting difficult. Some things you can try:

• Check with HP to see if there's a firmware update for your computer. If there is one, install it. You may also need to re-install GRUB after you update the firmware.
• Return the computer to the store and buy another brand. This is my #2 suggestion because the problem has existed for months and HP doesn't seem to have lifted a finger to change it. (#1 exists to give HP the benefit of the doubt; maybe they have fixed it, and I simply haven't heard of it yet.) This behavior calls out for action that will get HP's attention, and the best action to take to get the attention of a company is to return their problem products.
• In Windows, open an Administrator Command Prompt window and type bcdedit /set {bootmgr} path \EFI\ubuntu\grubx64.efi (change grubx64.efi to shimx64.efi if you're booting with Secure Boot active). This method works on some computers with similar problems, but usually not on HPs. Still, it's worth trying.
• Prepare a USB flash drive with rEFInd and test it. If it boots both Linux and Windows, reconfigure your firmware to boot from the USB flash drive by default and leave the rEFInd flash drive inserted in the computer.
• Run Boot Repair on the system, select the Advanced option, and click the check box to back up and replace the Windows boot files. This will cause GRUB to be installed in place of the Windows boot loader, and GRUB will be reconfigured to launch the Windows boot loader under its own name. This solution is an ugly hack, and some users have reported that Windows will sometimes undo it, so it's not really a reliable long-term solution.
• Install GRUB, rEFInd, or some other boot manager as EFI/BOOT/bootx64.efi on the ESP (that is, as /boot/efi/EFI/BOOT/bootx64.efi) and move or rename the EFI/Microsoft/Boot/bootmgfw.efi file to some other location. With any luck, your target boot loader will then launch. If you use GRUB, you'll need to reconfigure it to find the Windows boot loader wherever you moved it. If you use rEFInd, it will detect the Windows boot loader if you move it to the EFI/Microsoft directory.