1) Charge the Kindle battery. Charge it for at least an hour and see if the Kindle is working properly. If your Kindle was frozen due to low battery then this will solve your problem.
2) If your Kindle is still frozen go for a soft reset. Press Alt, Shift, R keys at the same time to do a soft reset. Your kindle screen would go blank and come back to life after some time.
3) If your Kindle is still frozen after the soft reset then you need to go for a hard reset. You can do a hard reset as follows:
- Make sure the battery is charged.
- If the Kindle is connected to power supply, switch off the supply and remove the charger cord.
- Turn the Kindle and take the grey cover off.
- You will see a small hole below the word "Reset". Insert a paper clip in the hole and press gently for about 10 seconds.
- Your Kindle screen would go blank and the Kindle will restart. If it doesn't happen immediately, give it a few seconds.
4) If your Kindle is still frozen after a soft and hard reset, you can try replacing the battery.
If your Kindle is still frozen after doing everything mentioned above, you need to contact Amazon Kindle support team. Log into your Amazon account, locate "Manage my Kindle" link and contact the support team by clicking on the support link at top right hand corner of the screen.
If you need any further assistance please ask :)