Perhaps just try booting into it's BIOS or booting from some kind of try-it-out linux distro like Ubuntu or Mint. You need to make a DVD with it on first or make a bootable USB data stick. Boot from it and see if the mouse/keys/touchscreen work ok.
They probably will and its probably just Windows 10 being rubbish.
Like ched says, try to get the proper drivers from HP for windows 10 for your laptop, uninstall the old ones and install the new ones. Also try another USB keyboard/mouse if you can.
You can test out these Linux versions without installing it or making any changes to your hard drive, just be careful.