Hello, It's not possible to know if the Kindle's at fault until you try another cable. However I'm going to give you a reboot to try and would like to see if that helps.
To do this, simply press and hold the power button on the Kindle for 25 seconds, then release and wait a full minute for it to reboot. If this does not cure the issue, oftentimes the reset procedure needs to be repeated several times for it to force a reboot.
If you're still running into problems, then try plugging the Kindle into the charger for 15 minutes, then eject it and try the reboot a couple of more times.
This clears up the issues you're having 90% of the times, but in the rare case that it does not, the problem may go deeper than a software issue. If this is the case, please reply back with the specific model number off of the back of the Kindle, and also how long you've had the Kindle for, and I will continue to assist you.
If you need further assistance let me know. Please do not forget to click the 5 STAR RATING, at the top of the page for my efforts. It is my livelihood and you can follow up at any time if needed.