I am Pete, and I'll be happy to assist with your question today.
1. Can you let me know which Kindle model you have, please?
2. Also, how old is it?
model no.001200 jc 9600a-1013 fcc id zee-1013, ca.3-4 years old
The battery may have failed after 3-4 years and will need replacing.
Try turning on the Kindle whilst it is connected to the power supply.
Also try performing a hard reset on your Kindle - press and hold the power button for 20 seconds and then release it. After the device has completely turned off, press the power button to restart it again.