Hi, Stuart:
The parts list for your PC indicates that it has a Ralink RT3090 wifi adapter.
http://partsurfer.hp.com/Search.aspx?searchText=XS971EA
The card is not supported on the newer releases of W10.
It completely disappears from the device manager, and there is no way to make it reappear.
You can see it by going to the device manager, click on the View tab at the top of the device manager window.
Select the Show Hidden Devices option.
Then look down the device manager list, find the Network Adapters device manager category.
Click to expand that category and you should see the Ralink wifi adapter in light shade.
You could try right clicking on it, select uninstall, check the uninstall driver box, restart the PC, and hope that Windows installs it so it appears normally in the device manager, but don't get your hopes up.
The easiest thing to do to regain wifi on your PC, would be to purchase an external USB wifi adapter.
This is the only W10 driver that Mediatek/Ralink released for that model wifi adapter and it is over 4 years old.
That card only worked on first few releases of W10.
https://ftp.hp.com/pub/softpaq/sp71501-72000/sp71571.exe