I also got this same problem like u. I have an iphone 4s, after updating ios 7 it was good for about 3 days. Then after 3 days suddenly my phone automatically switched off and white apple logo was blinking ,i was unable to switch it on. Besides the phone was not taking charge from the socket. And also was not connecting to itunes. Then i pressed the home and switch button together for about 7 seconds and turned it completely off. And now after 2 days this afternoon i tried to switch on the phone. And it was just a miracle that my phone automatically started to work. And now um enjoying my phone then ever.
I think u should try it like me, hope that will work.