From the Main Hall, use the Armor Key on the double doors on the second floor, directly above the main entrance. This leads to the West Balcony Corridor. Be cautious, as a zombie may be present.
Proceed down the corridor and take the first door on your right. This is the Medical Room. Inside, you'll find a zombie on the floor (often playing dead, so be careful). On a shelf, you'll find the Sword Key. Pick it up. Also, examine the desk for some Handgun Ammo and a First Aid Spray (a full heal item). Exit the Medical Room.