Why would he give up if there is a chance he can get it back?
The fact that he was on different IP should be nearly enough to get it back. I would send Jagex a quite long message (through the RuneScape website, not Twitter) and say something like "My computer had a malware ... I have lost my e-mail, paypal, facebook ... Is there no way you can see what IP my account were logged in from when it got banned? I can guarantee that it can´t have been my IP because I´ve been on a holiday for 2 weeks and everything was fine before I left and no one has been in my house."
something like that... I have recovered SEVERAL accounts this way. Try to make it very personal, sad and full of seemingly legit details.