There is a key for the door to get into the equipment room in vault 34, but I can't find it anywhere. Can someone help me out?

Need a key from the Boomer territory (in Pearls barracks) and then you ALSO need to drain the water in the flooded area.

I did this last night. Go to the two flooded areas on the fourth floor and search the dead vault technicians for passwords. Go upstairs to the room near the door to the armory to active the pump, which will drain out flooded areas. Go back to the flooded area past the clinic room and head to the newly water-free area. Go to the door marked Security... A (can't remember the second word), and go to the terminal which you can use to open up the Overseer's office. Go the Overseer's office, kill him, and collect his password. Finally, use his password on his terminal to disengage the armory door lock.

Thank you, no one explained the password was for his terminal and I never really checked to see. I was so heavily irradiated by the time I got back up there and couldn't get it open I had to get out. Thank you.