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So my sister recently got a iPhone 3g that was dropped multiple times. We ordered the parts that needed to be replaced which was the back case, new power button, and a new lcd screen. I tested the screen before I replaced the back case and it was working fine. I replaced the back case and power button and put everything back in. When i plugged in the screen it was still working, but then the digitizer pulled out. After that all i could get the screen to do is turn on and go white. What do I to fixed this?

What do you mean “pulled out” ? It stopped working or it had physically come loose? White screen issues are generally resolved by a battery reset. This means you have to physically stop the connection between the logic board and the battery momentarily (lift the logic board off the battery for a few seconds and then replace).