Q: Iphone 4s with new ios9.2 doesn't work properly

Greetings McJLin78,

So since updating your iPhone 4s to iOS 9.2, the phone's Camera app shows a black screen, but other camera apps work normally. Is that correct?

As you mentioned, that indicates that the physical camera hardware is functioning correctly, leaving us to troubleshoot the software. 

The following article has good steps for this issue - Get help with the camera on your iPhone, iPad, or iPod touch. You've already done some, but I would like you to do all of these in order -

You see a closed lens or black screen

If you see a closed lens or black screen when you open the Camera app, try these steps:

1. Make sure that there’s nothing blocking the camera lens. If you’re using a case, try removing it.
2. Force the app to close, then open the Camera app again.
3. Restart your device, then open the Camera app again.
4. If your device has a front and rear camera, try both cameras by tapping  . If you see the closed lens or black screen on only one camera, take your device to an Apple Retail Store or Authorized Service Provider for more help.

If these do not resolve your issue, since you have already indicated that erasing and restoring your backup also did not resolve it, the next step would be to Erase and set up as a new device. Follow the steps in this article - How to erase your iOS device and then set it up as a new device or restore it from backups. Do NOT restore from your backup.

Please let me know the outcome of your tests.

Thanks for using Apple Support Communities.

Be well.