Like any portable device, the iPhone is prone to freezing at times, or to having its software become corrupt. Most Apple devices revert to the Apple screen when frozen or loading, but seeing the Apple logo is an good sign. Even if your iPhone only displays the Apple logo, you then at least know the phone is working, that it has some battery life remaining, and you can troubleshoot it accordingly.
Whenever your device locks up -- which may be the result of a dead or dying battery or a problem with an application -- you can perform a manual reset to force the iPhone to shut down fully. Most iPhones don't shut off when inactive. Instead, the device enters a kind of stasis, waiting for input from its users. Press and hold the "Home" button and the "Sleep/Wake" button for at least ten seconds. The Apple logo should appear for a moment and then disappear, and the phone will return to the home screen.
Charge the Device
As the iPhone's battery slowly loses its charge, which can take anywhere between four and 40 hours (depending on use), it will react more slowly to input until it doesn't react at all. The Apple logo appears when the battery is nearly depleted as a way of alerting users that the device will soon turn off. Even if it does turn off, a few moments' activity might give the battery enough power to bring the device out of sleep for a moment. Plug the iPhone into your computer to charge the device fully, and it should resume its normal behavior after the battery is fully charged.
Restore through iTunes
As a regular part of the troubleshooting process, Apple included a software restore for the iPhone that must be accessed through iTunes. This process will back up all of your personal data and settings, and then wipe the software on the iPhone and replace it with the original operating system. Connect the iPhone to your computer with its USB cable and open iTunes, and then look for and click on your iPhone in the list of "Devices." Click the "Summary" tab along the top and scroll to the bottom until you see "Restore." Click "Restore" to begin the restore process.
Repair and Support
If you've tried troubleshooting the iPhone and it persistently sticks on the Apple logo, consider returning it to Apple or your wireless service provider for repair or replacement, as long as your device is still within warranty. For out-of-warranty products, Apple offers pay-per-fix service. Prices vary depending on the service; contact Apple support through Apple.com for full details.
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