When you first enter the room, the display is locked and the lock is broken. Ewan won't get around to fixing until you walk in and find someone breaking into the display from the other side --
Hint 2
-- which won't happen until after you get into Bridget's room and complete the dead drop.
After you listen to Ewan whining, go to the display and click on the controls, on the wall at the left of the display. (You might think you could just reach in through the hole Zoe made, but remember, that hole is on the other side of the display.)
Hint 4
This is one of those games where you want to remove all the colored squares, but they have to be in groups of at least two before you can click on them. Read on for a step by step.
Hint 5
These puzzles need to be planned out carefully. If you end up with just one square of a color, you can't ever get rid of it and have to start over.
Hint 6
When you get rid of a set of blocks, the blocks that were above them drop down. If you get rid of a whole column of blocks, the remaining blocks fall down, then slide left to close up the gap.
Hint 7
So if, for example, you have one red block on the left and one on the right, if you can get rid of the blocks in the middle, the two red blocks will slide together and be removable. If this is confusing, play around with the blocks for a while and see how it works.
Hint 8
There are probably other ways to do this, but here's how I did it: