So how do I open the door/are next to the main laboratory? The power is shut off
If you're talking about early on (and I'm gonna facepalm if so since that part's pretty easy and you're gonna have problems with the rest of the game if that's the case), then there's a power switch to the upper top of one of the rooms; IIRC, it's a bit hidden but it's also one of the easier "hidden" switches to find. However, since there are only like, two rooms at that point, it should be really easy to find with a bit of patient stumbling.
If you're talking about the laboratory deep within the complex, that one's hard and I myself couldn't find out what to do there for a while when translating: There's a room in the sewer (you need to have the ability to jump) that you must backtrack to, accessed by a large sewer pipe. In that next room (with a bunch of bookshelves), use the explosives (C4, which you can find as general pickups or by defeating enemies later on) to destroy the damaged wall and proceed. That part of the story is frustrating because there's no text in-game to tell you to backtrack or to find that particular room - it's one of the more crucial changes I made to the game by writing in some hints in the laboratory on where to go and indicating the sewer pipe and damaged wall with sparkling indicators.