If your phone is stuck at the Sony logo I would suggest that you first try to remove the SIM card, and then try restarting the phone. If the phone restarts successfully after you remove the SIM card it might be the SIM card that needs to be replaced. Secondly you could also try to remove the SD Card if you have one. If the phone restarts successfully after you remove the SD card, your SD card may be damaged and in need of replacement.
If none of these measures manages to get the phone out of the boot loop I recommend that you try to perform a software repair using a computer and Xperia Companion as @uliwooly mentioned. Please note that since the device cannot pass the boot screen, you need to start the repair without the phone plugged in and make sure to tick the box in the bottom left corner "My device cannot be detected or started, or is a Smartwatch 3" and then click on "Next". After this you should be able to follow the on screen instructions given by Xperia Companion.
As one of the requirements for a software repair to be possible is that the phone has a charging level of at least 50%, it is also a good idea to charge the phone for a while as @uliwooly mentioned
If the software repair doesn't help, contact your local support team in order to have the phone sent in 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.