I had this same problem.Without a power button, there was no way to turn my phone on. I charged my phone until it had a full battery, I then took my charger cord and plugged it into my PC, and it worked! It booted right up, and has been working fine since. It's an easy fix getting it back on, even without the power button functioning at all. Hope this helps!
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=== Update (12/16/2016) ===
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Well yes, try resetting it and then see if you can get "the right tool." Of course its going to be much cheaper than buying a new Kindle!
I had this same problem.Without a power button, there was no way to turn my phone on. I charged my phone until it had a full battery, I then took my charger cord and plugged it into my PC, and it worked! It booted right up, and has been working fine since. It's an easy fix getting it back on, even without the power button functioning at all. Hope this helps!