Before doing this you should buy the following skills: Chameleon, Shinobi, ECM Overdrive, Dominator.
There is a random amount of wire boxes in the FBI building. Two of them will disable the alarm of the room you need to enter. You have to get very lucky and cut the two correct wires. There is absolutely no way to tell which ones are the right ones and you are not allowed to use the computer. This is all about luck. The boxes change everytime you replay the mission. If you cut the wrong wire, the alarm will go off and you should restart immediately. The wire boxes spawn randomly. You should be able to get the right ones every 10-20 playthroughs.
It's important that you use your ECM Jammer to open the door inside the server room (requires ECM Overdrive skill). It will open the door silently and instantly.