Call Amazon Customer Service and tell them they just broke your PW-1 with a forced, OTA update attempt to 5.6.1.1 while the battery charge level was too low.
See also:
https://www.mobileread.com/forums/sho...49&postcount=3
The usual operation is for the Kindle to try doing its OTA upgrade at shut-down (or at re-start), but in this case, it probably fell into a low-battery re-start and tried to do the upgrade (with a dead battery).
It is toast, it is out of warranty, but it was their forced update that killed it, they are liable.