Hi @demosophist
What is the model number that is on the back cover of the device?
With Kindles it is easier to go with the model number rather than the model name and generation when trying to locate parts etc.
Backlights can sometimes be incorporated in the display and are not a separately replaceable part.
It could also be a blown backlight fuse on the systemboard or a loose display flex cable connection as well that is the problem and not the backlights themselves.