I've got a 2007 FPB that fades out - but I do not think it is a backlight/inverter problem.
The behavior is as follows: it works find for a while, then the display will start to slowly fade to black - always starting from the right side. It appears as if the *pixels* are all being set to black - not that the backlight is going out. Sometimes it stops part way across the screen and reverses to normal behavior. Sometimes the fade is accompanied by spurious lines, image jumping or other pixel related issues (not simply backlight).
If it gets all the way to black, it is not "full black" (i.e. turned off) - you can see what appears to be the glow of the backlight behind what appear to be black pixels. No sign of an image (using a flashlight, say). Eventually it returns to "good screen" - for a while and then it fades out again. This cycle can take from 5 minutes to 1 hour.
Behavior is the same with either digital or analog input.
The closest thing I can think of to describe it is a hot LCD screen (left in the sun for example) where the screen all goes black (due to the heat)
It would seem to me that something in the pixel driver circuit is shorting (or floating) to ground or Vcc and pulling all the pixels with it. I've searched on line and in this forum and see nothing that sounds similar.