Well, my display ended up looking like this after the repair:
As you can see, there was a light/dark banded pattern along the bottom of the screen, corresponding to the LCD's backlight. In my case it was also accompanied by a constant high pitched whistling noise. I swear to anything that's holy, it was not coming from the fan or the speaker, but rather the motherboard itself.
Anyway, both these problems went away when I disconnected and reconnected the connector at this stage. I'm saying this on the off chance it helps someone else.