Apple provides several troubleshooting steps to resolve nearly every issue with a frozen iPhone. If your phone is displaying a "Connect to iTunes" message, it could be a sign of a simple issue solved with some basic steps, or it may require a more invasive process such as restoring the phone to factory defaults. It is always best to begin with the simple steps to determine which will most easily resolve your issue and get you back to being productive with your phone.
Power Cycle and Reset
The first troubleshooting step you should try is to power cycle your phone. Press and hold the Sleep/Wake button until the "Slide to power off" message appears. Slide the switch on the screen to power off the phone, then turn your phone back on to see if the issue is resolved. If your phone will not react to the Sleep/Wake button and will not power off, then press and hold both the Sleep/Wake and Home button on your phone at the same time for several seconds until the Apple logo appears. Release the buttons when you see the logo and allow your phone to reboot to see if this resolves the error message.
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If your phone continues to display the "Connect to iTunes" message, then you will need to restore your phone to factory settings using iTunes. Launch iTunes on your computer, connect your phone using the USB cable and click "OK" when iTunes alerts you it has detected a phone in recovery mode. Click your phone's name in iTunes, then click "Restore iPhone" in the Summary tab. Click "Restore" on the alert window that appears. The restore process will begin and will erase all the data on your phone.
This process may take some time, sometimes up to an hour, which is mostly due to the size of the iPhone image that is downloaded from Apple. The progress bar will tell you how close the process is to completion and an alert window will appear when it is done. Following the restore, you can apply one of your iTunes or iCloud backups to your phone to restore your data.
If the factory restore process did not completely resolve your issue then you can attempt a similar factory restore using the iPhone's "DFU mode." In this method, the phone is put into a different state than with the previous factory restore. To place your phone into DFU mode you must connect your iPhone to your computer, then press and hold both the Sleep/Wake and Home buttons for 10 seconds. At exactly the 10 second mark, release the Sleep/Wake button and continue to hold the Home button until iTunes discovers your phone. Release the Home button, then follow the same factory restore steps from the "Factory Restore" section.
Technical Support with Genius Bar
If all of the above have failed to resolve your issue, then you should make an appointment at the Apple Store Genius Bar to have the team there diagnose your phone. The tech support team has access to factory diagnostic tools that can better determine the problem with your phone. Following the diagnosis they will be able to resolve the issue with your phone; if your phone cannot be fixed, they will help determine how to get you a replacement based on the status of your warranty.