I also check for BitcoinCore or another software that was installed maybe finding some crumbs of bad deinstallation,
but he has never uninstall something, and has only the standard programs and office pack on the pc.
If we assume that what you say is accurate - he has never uninstalled anything and there are no traces of a bitcoin wallet on his computer - then is there a chance these are not private keys at all, but rather passwords or some other important details for a web wallet? Is the computer you have access to the same one he was using back in 2013? Can you check the browser history for any web wallets or other bitcoin related sites which might give you a clue (or even other wallet sites which might give a clue as to any wallet software he was using)?