Hi and Welcome. My Name is ***** ***** I look forward to assisting you today with your question.
First we can can soft-reset the Kindle and see if it works or not. On Kindle, press and hold down the Power button for 40 full seconds and this will reset the Kindle. Restart your computer and then connect it to your computer with different USB cable and to different USB port of computer.
Unlock the screen of the Kindle and does it recognize now in Computer or This PC ?
Please let me know if that didn't work, so we can continue troubleshooting.