My Cinema Display bit the dust, and all the symptoms seem to point to the 150W power supply brick, which is apparently not an uncommon problem with those models.
New power supply bricks are close to $200. Ouch. Usually one bad component in a power supply is a lot cheaper than that, and I've soldered together a power supply or two in my day.
Unfortunately, the Cinema Display power supply is built like the monolith from "2001", with no apparent way to open it. Can I use a thin putty knife to crack it open, like the old Mac minis? Is there some way to get in through the line-in plug? Is it sealed in a way that can't be opened, but maybe there's a safe(-ish) place to saw through to get inside?