Floor 35 was the floor where John McClane met Hans Gruber physically, found several C-4 explosives planted, and fought Karl in a brutal battle. It is the floor that gains access to the rooftop of Nakatomi Plaza.
Hans Gruber is seen walking on the 35th looking for the man who has his explosives. He leaves his Walther PPK pistol in a hiding spot to pick up later. As he jumps down, he sees two bare feet of a figure lurking on him. Looking up and discovering who it is, Hans tricks the man with his MP5 in his possession that he is a hostage and lies that he somehow managed to get out from the 30th floor and ended up where he is.
The man reveals himself to be John McClane and when he asks for Hans' name (he is fooled by his American accent), he hesitantly replies "Bill Clay". McClane finds out he must be Hans Gruber and quietly empties the magazine from his Beretta 92F before giving it to Hans.