This looks very much like a hardware problem in the connection between the screen controller chip and the screen or within the screen itself. If you're lucky, it's the latter, and swapping in a new screen assembly might do the trick. But given that the screen is the biggest cost factor in eReader devices and you're out of warranty, this may not be cost-effective.
So unless you're really good with electronic hardware (or know someone who is), your best bet is probably to start looking for a new device, since finding someone who can repair this, and for less than a new device would cost you, seems rather improbable to me.
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