Hi, Did you disconnect the battery and make sure the phone was powered off when you replaced the display assembly? I have seen iPhone's not boot up properly or not display anything or display a white screen if the battery was still connected and the phone's power was powered on when the display assembly was connected. Could be the power button was pressed accidentally when the display was disconnected and the battery still was connected to the motherboard. I recommend making sure the phone is powered off before opening. Then disconnect the battery connector from the motherboard when you do the screen replacement? Then disconnect and reconnect the digitizer and LCD screen connecters to the motherboard and make sure they are connected tightly and reconnect the battery and power it on. Hope this helps.
iPhone 4 Display Assembly Replacement