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Do your cables work with a different device, not the Kindle?
There are different types of USB cables. There are (1) Data cables (these allow charging as well), and (2) Charge-only cables (these do not allow data, and the symptoms will be exactly as you described in your initial post).
Possibly, are you using charge-only cables? This is why I asked my first question - do your cables work (for data) with other non-Kindle devices?
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