Apple iPhones running on OS X iPhone derived from Mac OS using Darwin foundation (having four abstraction layers) can sometimes simply freeze on the Apple logo during boot up phase. This can be fixed by an easy troubleshoot if you know the basic functionality of iPhone.
So here we go:
Press Sleep + home keys simultaneously until the phone reboots.
Holding down the home button connect the iPhone to the computer/laptop via USB connector.
When you perform the above steps you can now enter the backup and recovery mode, this way you can restore the firmware of your iPhone and it all done.