On a jailbroken Kindle you could try running fsck on the command line to check for bad blocks. I'm not aware of a way to do that without a jailbreak but you might want to do a search to see if anyone has a workaround.
As pointed out already it would be cost-prohibitive to repair if you are outsourcing labour. It might be viable if you happen to have SMT soldering rework tools & expertise yourself.
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