Cannot turn my Kindle OFF

My Kindle is not taking a charge, probably due to a damaged charging port (Kindle was dropped while plugged in).

One of things I had read to try (before assuming the charging port is faulty) is forcing the Kindle to turn off by pressing the power button for 20 seconds. This did not work...it was still on. I have tried this several times to no avail. I have even held the power button pressed in for over a minute...it refuses to turn off.

What could be the problem?

Thanks!