Ok I know this is a bit late to respond since the OP probably did something about that iPad, but in anycase, I sort of found the solution! I believe it is something to do with the actual connector on the logic board that the digitizer plugs into. What the OP described is exactly how this iPad that I just received works. First thing I did was test it out and restore it to iOS 7, still acting crazy, some zoom option trying to prompt me to enable it, but the touch is unresponsive. So I turned it off (power plus home buttons together for 10 seconds), got my handy blow dryer, suction cup from the shower hanger, lol, a tiny philips screwdriver, 12 pack of soft nylon guitar picks, rubber gloves, plastic wrap, and a can of compressed air. So I fired up the blow dryer on highest setting, ran it around the digitizer's frame, popped on a suction cup on the right side, lifted up the glass a bit to insert the first guitar pick, and swayed it a bit to place 2 more around it, slowly making my way around the digitizer and...