I need the original product key for my desktop

[SDG78]

I bought this PC at least 7 years ago. It had windows 8 and has been through all the upgrades and was 10.1, but was really bogging down. So, we backed up our files and I RESET the PC. It is back up but reverted back to 8 and I can't find a product key to get it activated and upgraded back to 10.1. I can't find the original discs that have the sticker. I have tried the BIOS reading and it says nothing. Microsoft said I need to contact MFGer to get the original KEY, then they can help me. How do I get the Key, or get ahold of a human at HP that can give me the key by the serial number?

[Prométhée]

Hello
once again, I don't understand microsoft's recommendation.
All professionals must know that the product key, since Windows 8 is registered, in the bios, nobody can give it.
There are software that can recover it.
That said, there is no need to have the key, normally to install windows 10, it is clearly written at microsoft!

https://support.microsoft.com/en-us/help/12440/windows-10-activate

[WAWood]

@SDG78 

The problem you're running into is that the Win10 in-place upgrade has a history of corrupting the HP recovery information so even though the PC might look like is restored OK, in fact, there will be troubles and some stuff is simply not going to work properly.

It is likely to need a complete reinstall from Win10 media, not just the manual entry of a product key, to get it working again.

But if you want to try the second, you should be able to get the key using this utility:  ShowKeyPlus - Windows 10 Forums

Once you have the key, you can then try manually entering it using the link that @Prométhée provided you.