I'm having the exact same problem. I've replaced the screen, re installed the original battery, tried another battery, tried 2 more different screens. I even restored it with iTunes. NOTHING WORKS! I can't see how this could happen from simply changing out a battery. All connections look good and clicking in as they should be. FYI: all my parts are high quality from etechparts.com
Hopefully someone can help me with this matter...thanks in advance
Woodzyvision