After you've visited the culture center, the ship, and the pub --
Hint 2
-- talk to Dagny, and she'll ask you to fix the heater she's huddling under. Read to the end of this hint for a picture showing how to do this.
Hint 3
After you talk to Dagny, click on the top of the lamp-like thing she's standing next to start the puzzle.
Hint 4
Nancy's right when she says this isn't how "electricitology" usually works. But hey, it's a cute puzzle. And while you're solving, Dagny talks nonstop, and you might learn something about her and Nancy both.
Hint 5
What you're doing is arranging the five pieces across this board so that they create the five numbers shown on the bottom of the screen, based on the positive and negative numbers each piece covers.
Hint 6
For example, if a piece covers 7, -2, 4, and 0, its number is 9 (7 - 2 + 4 + 0 = 9), and the square at the lower right corner of the screen shows this number.
Hint 7
When a piece makes one of the target numbers, it's checked off in the "Targets" list. But there are multiple ways to make each number, so just because a number is checked off doesn't mean it's in the right spot.
Hint 8
There may be other ways to do this, but here's what worked for me:
Dagny also tells you that Elisabet keeps the cabin's key in her purse. Guess you'll have to find a way to distract her so you can root through her stuff.