Here are some possible solutions.
Do they work in the BIOS page? If yes then it could a Windows driver issue. Check in the Device Manager. They may have or not have an exclaimation mark by them. Regardless just uninstall them and let Windows re-install them.
The other thing could be the keyboard locking. Not sure if on your model. Try pressing and holding the ***''right Shift key''*** for 8 seconds. Doing this should unlock the keyboard. One of those "features" on some HP machinies!
Turning off ''Cortana'' also sometimes helps.
Disabling ''ctfmon.exe'' (Windows Collaborative Translation Framework), which is for multiple input methods, may also work.
Another thought. Does the onscreen keyboard work? Look in Settings.
Let us know how it goes.