If he's dumb with computers you could just open your case and unplug the power button from your mobo....Unless he plugs that in he wont be able to use your computer.
Other than that just tell him to stay off your computer...Say that you have tracking software and you can see if he goes on there and what he's doing.
setting admin and bios passwords would stop him from getting in, but you said you wanted proof if he is or isnt, so that isnt an option really. post 9 looks good to me
I looked into the same thing a while ago... http://www.kmint21.com/keylogger/
Is a good choice. Works quite well. Personally I'd go with the suggestion of a BIOS password, but it's up to you.