Although this is a mess, mostly because the dealer (assuming this is NOT a player dealt event) did not do his/her job, the short answer is that the SB gets the pot. The BB player CANNOT win the pot, in fact his hand should have been declared dead and mucked as soon as the button received his/her 2nd card. Had that been done properly (according to the rule you provided) there would be no need for this discussion.
Hope this helps!!