If your iPhone is showing a black screen that never goes away, you should try resetting it or putting it into recovery mode.
The screen is a critical component of the iPad, so it can cause a lot of panic when it suddenly has issues. Aside from the button or two on the sides of the iPad (and a Home button on older models), ...
If your iPad screen won't rotate, you might have to turn off the Orientation Lock or do some other troubleshooting.