phone is open but the touch screen is not working

I've seen this only a couple times! It's a strange issue. I would try a soft reset first to see if it's just frozen. You can perform a soft reset by holding the power button, volume down button, and home button at the same time for about 15 seconds.

That works about 50% of the time. If it's still stuck after a reset, then I would take it into a shop to get it diagnosed. Taking it apart on your own is quite the task, but doable if you're willing to destroy the phone.. As the back is glass, and is super hard to remove without breaking. I would look into a warranty replacement through your carrier if the problem turns out to be the screen itself, as the part alone is about $150

Also, is it possible any water has gotten inside it by chance? I see this mainly after the phone has been in contact with water.