If none of the previous solutions works (the most important troubleshooting steps), I have good and bad news for you (please don't shoot the messenger).
Bad news is that your Kindle is defective (defective charging port or bad battery). I have provided you with the all troubleshooting steps for resolving this kind of issue (resetting the software, force reset, USB charging). Unfortunately there is an hardware issue on the device that software troubleshooting can't resolve. Because defective port is the main problem in 95% it's not a good idea to replace the battery without testing the Kindle.
Good news is that if your Kindle is still under Amazon warranty (1-year warranty) you will receive a new Kindle for free.
If your Kindle is out of warranty, the good news is that Amazon does often replace Kindles out of warranty. At least they would replace it for less than the cost of repairing.
You will have to contact your seller/retailer or Amazon warranty support service to arrange replacement.
There is an option that Amazon calls you. To contact Amazon use the procedure below.
1. Go to the page below - click here
Log in using your Amazon account information.
2. Select Kindle > Kindle Device (or Troubleshooting my Kindle) > Problem with my Kindle > My Kindle is damaged or Kindle is frozen/unresponsive
3. Click Phone - Call us
4. Enter your number and choice "Call me now" or "Call me for 5 minutes".
Sorry I could not be of any more assistance, but there is a hardware issue that can't be resolved online.
Please let me know if you are not satisfied with my help or if you need more information. I'll be happy to help with any follow up questions.