There are really two different issues here regarding restoring your PC.
The first is license. Your PC came preinstalled with an HP OEM version of Windows. The product key embedded in the firmware of the motherboard of your PC will only work with that version. If you restore using any other version, that is likey to be a Retail version, and that will require a Retail license to activate -- which I presume you do not have. The HP license will not activate any Retail versions.
The second is Windows release. I have a retail version of Win8 and that product key worked with both Win8 and Win8.1. But you have an OEM version, and I do not know if that license will also work with Win8.1 -- it might not.
Your best bet is to use HP Recovery Media to restore your PC, not something else you bought or downloaded.
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