Kindle Fire screen won't light up after a fall.

I slipped on the ice while holding my Kindle Fire and now my screen won’t light up. I didn’t think it hit the pavement, but I badly scraped the hand I was holding it in, so maybe it had a worse fall than I thought. It was in its case, so there was no exterior damage.

I tried pressing the power button and holding it. It made that sound it makes when it asks, “Do you want to power off your Kindle?” but there was no image on the screen. I tried touching the screen where the “yes” and “no” buttons usually appear, and after a couple of tries, I think I shut it off. Now, as far as I can tell, it won’t turn back on again. I’ve plugged it into the charger to see if the screen would light up when I did that. No dice. Suggestions?