You cannot delete your FARK account, and they are very clear about it.
From the FAQ (http://www.fark.com/farq/faq/#I_don.27t_like_my_login_anymore_and_want_it_changed.2Fdeleted).
We can’t help you out with that one, unfortunately. We don’t delete logins and we don’t change account names. Unused or seemingly abandoned accounts are not available for “recycling.”