Answer to "Replaced battery, phone turns on, screen doesn't?"I know its a long shot, but there is a protective film on the _inside_ of the screen. I forgot to remove it from my I pad and touch wouldn't work. It was fine after I removed it.
Answer to "Replaced battery, phone turns on, screen doesn't?"If you shine a light onto the screen can you see a faint image? If so, then the LCD connector was not inserted properly. It will need to be re-seated. Try it, even if it looks fine. In these tiny devices a hair's breadth makes all the difference.
Answer to "digitzer is not working after replace"Did you remember to remove the protective plastic on the inside (underside) of the digitizer? It won't work with that in place.
Answer to "replaced ipad 2 digitizer but its not working?"I just replaced a digitizer on an ipad 2 GSM and had the same problem. On closer examination, I realized that I had not taken off the protective plastic shield on the inside of the digitizer. Once I removed it, all worked perfectly.