Sorry to hear about your problem. To be honest this is an ongoing issue with the Kindle's hardware but before I get into the details, could you please try holding the power button for 30 seconds while the Kindle is being charged?
Thanks and Regards,
Ok, how old is the device?
Sounds good. Just one last question. Your Kindle boots to the logo and then shuts down?
Ok. Can you try connecting to your computer using the USB cable?
Does it work after connecting to the computer?