If you're trying to do a clean install of a free Win10 "upgrade" you may be encountering some of the issues with trying to do that--as it's something Microsoft doesn't really want you doing. It's generally recommended to do an in-place upgrade first, let the system become registered with Microsoft (which some say can 24+ hours) and do a backup. Then you need to follow a fairly specific procedure to do the clean install when you don't have a Win10 product key. There are many guides easily found with a Google search.
It's also possible, even with a paid Win10 license, your BIOS is too old, doesn't correctly support EFI, secure boot, etc. You might see if there's a bios upgrade for your HP and/or if it's known to be Win10 compatible. I would also try resetting the BIOS to the factory defaults if your HP has that option.
A third possibility is that while your drive is passing diagnostics, it may have some strange OEM or other partitions on it that are interfering with the new install. You might consider making a USB bootable version of the current free Ultimate Boot CD, or one of the free bootable partition editors, and verifying that your drive doesn't have any unwanted partitions. Beware if you wipe out any HP OEM partitions you may lose your OEM copy of Windows.
A final idea is Win10 could be corrupted on your USB drive. That happens more often than you might think--usually either due to a (perhaps invisible) problem while it was being downloaded or the USB drive itself is marginal. Again, if you can use the download to first do a successful in-place upgrade you'll know you have a good download and files.