Step one: Re-charge the battery.
Yes: I can see in your post that you have already read about that, but now your situation may well be different.
Either (or both) of two things has happened:
The battery has been over-discharged enough that it can no longer hold enough charge, OR
The battery has been discharged to the point that the internal battery management can no longer re-charge it.
Remove battery from Kindle, recharge it with an "Amazon Approved" re-charger.
That is the "official" company line.
For DIY situation - you can use any general purpose Li-Ion charger, OR
You can "fake it" -
Use a constant current, voltage limited, charging source;
Recharge at 30% of the listed (on the battery) one-hour rate for two hours.
Do not exceed a terminal voltage of 4.2 volts under charge;
Do not let the temperature of the battery raise enough to damage it.
That **might** (if not suffering from lack of charge holding capacity) get the battery back to a condition where you can get the Kindle into the "fastboot" re-charge mode.