Why is my Moto X not powering up?

A couple weeks ago I dropped my Moto X. It has a rubber protective case and there was no visible damage but it was not powering up. Even if I held down the power button for 5 minutes it would not start up.

Just to experiment I tried connecting it to a higher power USB charger for a bit. At this point it showed the battery charging at 1%. This suggested that the display was working and somehow the fall discharged the battery (I don't know how that is possible).

Once I charged it up I held the power button for several minutes and eventually it started up like normal.

Unfortunately yesterday the phone got dropped again in similar fashion. Optimistically I tried the exact same approach but this time the phone is not powering up. I have connected it for an extended period of time to the same charger and held down the power button for over 5 minutes and it still does not do anything.

Any suggestions on what might be wrong and what I could do to fix it.

Again, thanks to the protective case there is not obvious visible damage. I did try opening the back cover just to take a look but closed it without really doing anything.

I hope you guys can help me get my phone working again.