Having a similar version of the same problem, but I have 2 questions. They may seem like detail nit-picking, but they're still options not mentioned earlier and approach this for a different request.
If there is no way to remap a single key, is there a way users can just create a file that makes a whole new keyboard (but uses many of the same mappings.)
Is there a Windows setting (or other option) that can change the use of the F1-F12 keys to use/not-use the FN (function) key? For example, most computers I've seen (including the one used to type this message) have the F2 key in Excel open the highlighted cell by pressing F2, but his laptop requires FN + F2 because plain F2 dims the screen.
I've searched for 3rd-party software, but between the mixed-success results and the fact that some don't show the F1-F12 keys at all, I'm strongly favoring a Microsoft-centered answer. Since HP was able to change the keybindings from the default setup (and since the change would be Back To the default,) there should be an easy way to reset them to Microsoft's default.