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No, don't open the phone or take out the battery. It has an non-removable battery. It seems like iTunes tried to update the phone but couldn't do it successfully and that corrupted the system files. We may need to do a restore.
First we can reset your iPhone
and see if it works or not. Disconnect it from your computer. Then press and hold down the Power button and Home button at the same time until it shows the Apple logo. When you see the Apple logo, release the buttons and let it boot.
If it is still boot into iTunes logo screen, that means the iOS system is corrupted and you need to restore.
So connect it to your computer and open iTunes. iTunes will say that it has detected an iPhone in recovery mode and ask you to restore it. So restore it.
If it doesn't ask you to restore it, then follow the steps below to restore your iPhone by putting it to DFU (Device Firmware Upgrade) Mode.
First download and install latest iTunes on your computer from here : https://www.apple.com/itunes/download/
Then connect the iPhone to your computer with the USB Cable.
Open iTunes application on your computer.
On your iPhone press and hold the Home button and the Power button at the same time.
After EXACTLY 8 seconds release the Power button. Continue holding the home button until your iTunes shows a message telling you that it has detected an iPhone in recovery mode.
Click OK or Restore
Note : Put it to DFU Mode while connected to computer and also in DFU Mode your iPhone will remain blank and will be unresponsive. It is normal. Timing is critical when you put it to DFU Mode. So keep trying until it goes to DFU Mode. And it will take a while to restore it.
Please let me know if that didn't work, so we can continue troubleshooting.