Level 1: Locker room
The socket is for a light bulb so you may see what you are doing in this Broom Cupboard. You need to find it (again).
There are no more light bulbs in the locker room. You need to get the bulb from the first Broom Cupboard. You can take it from the level 1 cupboard and bring it downstairs and plug it in.
What do I do with Krytens other arm?
At this stage nothing. It becomes part of your inventory until it is required.