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Can you check if the same problems occur in safe mode?
http://talk.sonymobile.com/t5/FAQ/How-to-boot-your-phone-into-safe-mode/m-p/348008
Can you elaborate a bit? So when you tried to turn it on,what happened? You said something about standby,now you say about rotation.
Does your phone has a protective case or film?
you could go to a Verizon store to get it checked up or contact Sony directly but before you do that, backup everything (if possible) and repair your phone with PCC
Bridge (for Mac)
Alternatives on How to backup Xperias
If nothing helps you, I will give you the steps for the repair mentioned by uli above.
Performing a software repair using PC Companion.The process will erase all internal memory.You might need to charge your device for about 1-2 hours before so the device has at least 60% battery.
Make sure the device is not connected to computer or laptop and turned off (sometimes you have to press power button and volume up until the device vibrates 3 times or on some devices you have to press the small button near the SIM tray or on the back of the device).
Open PC companion->support zone->phone/tablet software update->repair my phone/tablet blue highlighted.Follow the steps given,do not connect your phone until prompted to press volume down while plugging USB cable. If PC companion does not start the repair process, you might need to run it in compatibility mode with Windows 7 (in some cases XP).