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I turned off my phone yesterday and after 30 minutes I wanted to turn it on again but it wouldn't start. I tried holding power button+volume up/down but nothing happened. Thought the battery may be drained out so I connected it to a charger and the LED lit up on steady red color but the battery charging percentage wouldn't show up. I've left it for 3 hours but it still wouldn't turn on or respond to Power button+Volume up/down and the LED still shows red while connected to a charger and turns off immediately when disconnected . I also tried repairing it using PC companion but neither the PC or my Laptop would detect it.
Exactly the Same problem as yours.! Please Say me here if you find some solution.. Thanks in advance..
Hi @HPSH, I'm sorry to hear about your phone. 
Could you please try and and press the volume up button and the ON/OFF button at the same time for about 10 seconds, this will force your phone to be turned off and you will receive a few vibrations.
Try and power on the phone as normal with the ON/OFF button, is it starting now?
If it's still not powering on I would recommend that you remove the SIM and/or SD card from your phone and then try and start it up again.
Let me know how it went! 
I have the same problem.. I've been doing all what you said in this post for past two weeks but of no use.! Same problem is being found by many Xperia C users round the globe.! Sony Support, You should look into this problem seriously as it is naturally suspicious to find same problem in many phones @ Jonas
Hi @nagarjuna97,
I'm sorry to hear that you experience the same troubles with your phone and other users as well. 
If you have done the troubleshooting that I and @nolramlb recommended, I'm afraid your phone will have to be sent to an authorized service centre.
I will not be able to assist you with this since I work globally, so please get in touch with your Local support and they will assist you with getting it in sent. They will also be able to answer all your questions regarding warranty, service routines and so forth.
Keep me updated! 