Here's a short walkthrough of the hospital:
- after getting caught, get through the pediatric ward and the others rooms until you reach the cafeteria.
- Once you get to the bridge area, seek a corridor guarded by a stationnary guards. There's a few way to distract him, the pmost obvious one being pushing a button in the adjascent room.
- Once you pass the guard, up the stair you can open a door in the small room that will lead you to the upper level of the big control room. Acctivate the terminal to open up the office.
- Go back to the bridge area, go through it to access the office
- In the office, you'll find in a small room a tech access ccard that will open up a door that will lead to the vents.
- The vents allow you to access yet another upper pathway in the big control room and open the door to the orthopedic ward
- In the orthopedic ward, follow the way and you'll get the croutch skill, that will allow you once you got back to the vent area to slip through a pipe and escape
I left over a lot of optionnal stuff to do, but here's the critical path. Hope that'll help you !