Just before Billy has to save Rebecca from falling into a chasm, Rebecca needs to pick up a note that says what the power settings need to be, in order to unlock the door.
But, when she falls into the chasm, Billy needs that note, because it hints how to open it. Below is a detailed walkthrough to help finish the task of saving Rebecca on that particular part of the game (courtesy of GameSpy.com):
As a word of caution, the hall that leads to the Basement is lined with giant spiders. They're not worth killing, but you also want to make sure you don't dabble around in the area too long -- if they manage to spit their venom on you you'll be poisoned until you take some Blue Herbage. The best way to make it is to split the team up, and run in one at a time until you reach the end. Just run your characters straight down the hall, then take a sharp left turn (stick close to the corner) and reach the door and the end of the hall. Once you've reached the Basement Safe Room examine the Green and Blue Herbs on the floor, take the Basement Map on the wall, and you might as well check out the Inmate List on the table (though it really has no pertinent information). There's an Ink Ribbon next to the type writer, so feel free to save your progress if you're looking for a good spot.
Proceed to the next room -- it's a bit sordid -- and find the corner with a small hole where you can give Rebecca a boost. She'll appear on the other side of the wall in an even more ghastly torture chamber. The door is locked, so read the notes on the ground near the door to figure out how to open it. Set the power regulator to 70.
To correctly set the power regulator to the 70 mark (indicated by the red arrow on the display) you'll need to play around with how each switch affects the needle. Or if not, you could just flip the switches according to this pattern: up, up, down, up, up.
Once the regulator has been activated, two doors will open (the one for Rebecca to get out, and the other door in the hall with the giant spiders) -- as well, the steam coming from the boiler room equipment (northeast corner of the first floor on the Training Facility) has ceased to bellow out.
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