Has it been opened?
Opening the case with a sharp object such as a knife can damage the display flex cable. I have one like that (free + shipping on ebay). I can see the sliced traces when magnified. I hope to fix it with conductive ink.
Because the screen only uses electricity when it changes, perhaps the CPU or something else is frozen. You could test the screen by plugging into a different kindle. The cable swings out of the case enough to do that, which is how I was able to activate the Voice Guidel setting (Setting page 2) by plugging in the screen cable from another kindle with back off.
Kindles are surprisingly usable with only Voice Control and Text-To-Speech (and jailbreak, of course)...