Kindle fire I only hear sound when I plug in the headphones

Kindle Fire: 12 Common Problems and How to Fix Them ...

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Mar 6, 2013 - If you are experiencing some Kindle Fire HDX problems then you might just ... Try deregistering your Kindle Fire HD by swiping down from the top and tapping More > My .... by Simon Hill: Updated to add sound problems, screen flicker glitch, ... Lion Captures A Baby Baboon But Does The Last Thing You'd ...

Amazon.com: Customer Discussions: Screen Flicker on Fire

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Amazon.com, Inc.Nov 17, 2011 - The Fire's screen should not flicker; if it does, call Amazon CS and ... *update* i called about my flickering kindle fire. customer service was ... Kindle Fire HDX 7 inch - Screen ...
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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.

Try shutting down your tablet or what ever it is and then wait like 5-10 or 15-20 minutes then turn it back on. It happened to my moms kindle fire and I fixed it lol.

Sounds like it should be returned, if still able to. There is most likely a cold solder joint or wire, but i dont believe it is user repairable.

Restart the FIRE (Press and hold the power switch for a count of 20)

Now start normally - if not cured call Amazon and expect a free replacement to be sent to you.

If the sound works on your Kindle Fire's speakers and will not cut off and reroute sound to headphones when you plug them in to the headphone jack port on the side of the Kindle. Try the following:

If you have a set of blu tooth headphones then enable blu tooth connection to a source of sound like, You Tube, Spotify iTunes etc. You will be able to hear sound on your blu tooth headphones this way. Turn of the blu tooth headphones, then try plugging in your regular wired headphones into the Kindle and reconnection should be achieved.

The Kindle Fire will not turn on, correct? Let's try a hard reset.
Step 1: Unplug the device from the charger
Step 2: Press and hold the power button for 30 seconds
Step 3: Release the power button, then press and release the power button normally, the Kindle should wake up
Step 4: If the Kindle does not wake up, find an alternate charger or go down to Radio Shack or Staples and get a new charger
Step 5: Plug in the new Charger to the Kindle for 12 hours when done leave the Kindle plugged into the charger
Step 6: While the Kindle is plugged into the charger, press and hold the power button for 30 seconds. Let the Kindle charge for another hour.
Step 7: Pickup the Kindle, press and release the power button normally, the Kindle should now wake up.
Step 8: If the Kindle does not respond, contact Amazon for a replacememnt

I am sorry to hear about your problem. So, if I understand you correctly, you have a Kindle Fire and a video that you would like to delete but since the Kindle Fire is full, no space left, you can not authenticate to WiFi, correct?
The only solution that I can think of it to reset the Kindle Fire to Factory Defaults and before the Kindle fully syncs with the cloud delete the Video.
Step 1: Pull down the upper status bar, select More+
Step 2: Select My Account - Deregister the Kindle
Step 3: Wait the above step can take up to 30 minutes
Step 4: When done, pull the upper status bar, select More+ and then select Device
Step 5: Next select "Reset to Factory Defaults"

It is possible that your Kindle Fire's battery has died. If you noticed the battery life diminishing before it wouldn't turn on at all this may be the case. Here is a site that has replacement batteries for the Kindle Fire:
3555A2L Battery for Amazon Kindle Fire D01400