I charged my kindle, but can't get it to turn on

There might be the issue with the Kindle device. You need to scan the device and check the issue. Ask for the support to amazon if you have some panding issues with your kindle device Kindle Technical Support Registration 877 690 9305

According to Love My Kindle Fire, nearly every Kindle owner will, at some point, need to learn how to "reset" their machine.
"When I hear (or read) these words from those who are experiencing a problem with their Kindle Fire it usually ends with something like, "turn on", "charge", or "work".

If suddenly your Kindle Fire won't work, then its most likely locked up. However, sometimes when it locks up, you can't tell because the screen goes dark (either gray or black). It just looks like it's off when in fact it is already one. cause the screen goes dark, either gray or black. It just looks like it's off when in fact your Kindle Fire is on but is stuck. When an electronic device locks up or freezes usually resetting it fixes the problem. Resetting your Kindle Fire is actually really easy, just hold down the power button for at least 20 seconds. .If your Kindle Fire won't turn on it's possible the battery went dead (if it was left "on" too long).
Plug in the power charger and wait about 15 minutes to make sure it gets enough charge, and then try turning it on again.
If it still won't turn on, try to reset the Kindle Fire again to be sure it's powered off.
If it still won't work, try someone else's charger, in case yours died.