We've seen a lot of these displays fail more recently. The issue is, there isn't really a reliable source for the parts of these displays. Apple class all the cinema display models as 'Vintage' now (even the thunderbolt 27" model), so the only option is after market sources, which dry up pretty quickly...
That being said, if you shine a torch on the display and can see a faint image, and the mac can see the external display as being connected (check under the 'Graphics/Display' tap of the system profiler, or system information panel. it should show up showing the display as being connected with its resolution noted, even if the external display is blank)
if that is the case, then it is more likely to be one of 3 things. The LCD having failed, the internal logic board or the PSU. The all in one cable does wear and fail on occasion, but in our experience, this causes intermittent connection issues, so it wouldn't be showing up in the system information panel, and wouldn't be showing a faint image.
Basically, 2 feeds go to the display, so its helpful to know which has failed. You get backlight feed, and you get image. If you can see a faint image, then your backlight feed has failed.
Same goes for your display @schwinny. It is likely that your backlight feed is beginning to fail, so it will need tracing, but its a separate issue to the image feed, which is unaffected from what you've noted in your symptoms.
I hope this helps.