3gs iPhone froze at boot screen (apple logo)

Don`t worry. This is just a common problem.

1. Force Restart iPhone Press and hold the Power button and Home button together until you see the Apple logo appear on the screen.

2. Put Your iPhone into Recovery Mode
Step 1. Connect your iPhone to PC and launch iTunes. Hold both the Power button and the Home button at the same time.
Step 2. You will see the white Apple logo coming up. Do not release the buttons until the Connect to iTunes screen appears.

3. Use iOS System Recovery software like TunesKit iOS System Recovery..., which can fix iOS system problems without data loss.

4. Put Your iPhone into DFU Mode
Step 1. Run iTunes and plug your iPhone to the computer. Slide the button of slide to power off to the right to turn it off.
Step 2. Press and hold the Wake button for 3 seconds. Keep holding the button and hold the Home button at the same time for about 10 seconds.
Step 3. Release the Wake button but continue holding the Home button for another 5 seconds. If you see the screen turns black, then you have already completed DFU mode.

There are actually different causes that will lead to iPhone stuck on Apple logo. However, it doesn't mean that your iPhone is permanently broken. Here are some solutions to fix your iPhone stuck on Apple logo issue.

1. Charge your iPhone for at least 30 minutes to make sure it is not caused by a drained battery.
2. Force restart your iPhone to exit Apple logo. The steps are differ on each model. For detailed steps, see: Force Restart iPhone - iPhone User Guide
3. Restore your iPhone in recovery mode with iTunes. For detailed steps, see: Restore Your iPhone in Recovery Mode - Apple Support
4. One-click to troubleshoot all software issues by iOSFix, a certificated iOS repair tool to fix all software issues of iOS devices and Apple TVs.
5. Contact Apple for hardware repair.

Since iPhone has turned off the authentication before ios5.1.1, they can only use the firmware of ios5.1.1, but now 5.1.1 has been jailbroken perfectly, so don't worry, it just about jailbreaking.

IPhone Stuck on Apple Logo Best Three Solutions for You
Many factors may cause this problem that you can't foresee, so we have to prepare some alternatives to solve the problem when your iPhone 5s, iPhone 6 (Plus), iPhone 6s (Plus) iPhone 7 (Plus) stuck on apple logo.
Just see the following tutorial about iPhone stuck on Apple screen.

Find your solution from the list,
Apple Iphone Smartphone
Codes:

• Unlock Code,
• Password,
• Puk Code,
• Lock Code,
• Other Codes.

• Software Problems (Hang, Youtube etc.)
• Hardware Problems (Display, Charging etc.)

Re-download the ipsw file that was on your iPhone, Download Spirit to jailbreak, and that should do the trick.