Your title and description are a bit conflicting. You say the screen is black, which leads me to think you can't see the icons. That sounds like the LCD is broken.
Then you describe the screen as being able to see the icons, but they don't respond to touch? That sounds like the digitizer is broken.
But calls and texts are still being received and I guess you are answering the calls and texts? Or they are just being received?
Sounds like you need the touchscreen assembly replaced. That is the top glass, digitizer and LCD assembly all made together.