The Turret in the locked room to the left begins firing through the window. Let it shatter the window glass, then hit it with Electro Bolt to stun it. Jump onto the ledge and crawl through the window to hack it. This lets you explore the southeast corner of this wing of the Medical Pavilion to find the Speedy Hacker tonic.
Locate the ventilation shaft near the floor in the corner of the room and bash it open with the Wrench. Crawl through the opening above the pipes to the locked office and use the Pistol to shoot the fuel cylinder the Leadhead Splicer is sitting on. Scour the room for valuable items and be sure to grab the Auto-Hack Tool off the desk, then leave through the door to the left. The door to Chompers Dental Office in the southernmost area of the floor is currently locked, so head to the Health Station and go through the door to the Dandy Dental area.