The computer room is in the north-west section of the residential area, marked as #3 on the map within the residential area. There are two major tasks here.
Dr. Eminess is hiding in one of the rooms. To get him, to talk, move the depository box adjacent next to the door - he will make a short speech about you needing to get into the library. He mentions that he will need a saw.
If you do not have have the saw, you will need to return to the Residential Corridors. Follow the corridor in the north, until you see a door on your right saying "Armory". In the map, it's annotated with the label R109.
In the armor, pick up the saw. This will activate an enemy who will patrol around the armory, and will not despawn until you escape. Simply wait for the zombie to walk way from the door, and return to the computer room.
Before you return the saw, explore the area first. When you place the saw into the depository, Dr. Eminess will take it, but will change into a zombie and attack. To escape him, head to the far room, and open the door on the right into the cold server room. Lure the zombie into this room, and close the door with the zombie inside. The zombie will remain trapped here.
You can now enter Dr. Eminess's room, and retrieve the saw, but you won't have the hand you need.
There's some notes on the computer, but the computer is offline. You will need to fix the computer by locating three network cards. You will also want to locate the server manual to learn how to configure these cards.
The server installation guide is found in the middle room, which describes the cards and software installation.
The Boot (red) card needs three programs installed: Circuit Setup, Disk Info Setup, and Hardware locator.
The Network (blue) card needs five programs: Circuit Setup, Socket Protocol, Firewall, Antivirus, and Net Locator.
The Interface (green) card needs four programs: Circuit Setup, CMD Interface, File Streamer, and Admin Tools.
These cards may be programmed in the computer just outside of the cold server room. Insert a card into the slot, and use the computer to assign the associated programs. When initialized, move the card into the server rack (after removing the broken cards).