If suddenly your Kindle Fire won't work, then it's 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 your Kindle Fire is on but is stuck.
This is usually why a Kindle Fire won't turn on or charge, because it's already on but is locked up and thus won't charge or work properly
How to Reset the Kindle Fire
Resetting your Kindle Fire is actually really easy, just hold down the power button for at least 20 seconds.
Unless the screen is black or gray, you'll know when it's off. If you can't tell, just be sure to wait a full 20 seconds.
When you're ready, hit the power button to turn it back on.
Kindle Fire Won't Turn On
Kindle Fire Power Cord for Charging
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.