Last time my iPhone 4 get into weird iPhone staring issue and instead of starting it was only showing Apple logo. I had no choice but to restore my iPhone using my backup file. I get into DFU mode and searched for iPhone backup files. This quick tutorial is useful for you if you are looking to find your iPhone backup.
Windows Vista or Windows 7 iPhone Backup Location:
To access this location in Windows, you may have to enable Hidden files & Folders because by default this folder is hidden in Explorer.
C: > Users > [Name of User] > AppData > Roaming > AppleComputer > MobileSync > Backup
Windows XP iPhone Backup Location:
C: > Documents and Settings > [Name of User] > Application Data > Apple Computer > MobileSync > Backup
Mac OS X iPhone Backup Location:
On your Mac, to find iTunes backup navigate to:
[User Home Folder] > Library > Application Support > Mobile Sync > Backup
This is something I was not aware of, and after finding the iPhone location it will be easy for me to restore my iPhone.