I believe (I'm not sure about this, so somebody correct me if I'm wrong), that the backlight of a TFT monitor is also built up in segments.

I've changed laptop backlights in the past and they have always been continuous tubes running along the top and bottom (or up the sides for that matter) of the display with a single diffuser in between. If a single tube fails then the display gets progressively darker from top to bottom (or bottom to top!) and if both fail (usually a circuit fault) then you can't make out any on-screen display at all. When I read the original post here it didn't strike me that the backlight was the culprit but I could be wrong.

Changing the FL tubes is the extent of my experience with TFTs but I've always believed that the active drive electronics are segmented.
Assuming that changing the display adapter doesn't fix this I'd bet on the electronics. The electronics can be fixed by specialist firms with the proper equipment but I don't know if that's economically viable.