You can turn off any Kindle Fire by depressing the power button continuously for at least 15 seconds. If the screen had been illuminated when you first pressed this button, then it will go dark while you are holding it down. If the screen was dark to begin with, then the device was already off, and the battery possibly depleted as well.
A second momentary press of the power button should cause the Kindle to start up, unless, of course, the battery was dead or the Kindle was otherwise broken. If the unit boots up then the freezing problem should be gone (for the time being, at least.)