Have you tried the testing the functionality of the hardware keys in the diagnostics menu? In order to do this, Find and tap Settings > Tap About phone > Tap Diagnostics > Tap Tests > Camera button/Volume up button/volume down button.
If the fingerprint hardware has stopped being available in the phone, I suggest that you repair the software in your phone using Xperia Companion. Please note that a software repair will erase all user data from the phone, so make sure to do a backup of your user data before proceeding with the repair in order to prevent data loss.
If the software repair do not manage to improve the functionality of the hardware keys and the fingerprint sensor, I suggest that you get in contact with your local support team in order to have your phone sent to an authorized service center. If you have any questions regarding the service, such as routines, warranty and consumer laws, these type of questions are best answered by your local support team as well, as they vary between markets.