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Did you check all the power connection any loose connection will result in the phone not starting. Also make sure that you do the home + power hard reset properly as I had the same issue. First hold down power and home simultaneously for about 10 secs, then release the power while still holding home for another 10 secs logo should come up. just replace my screen. took me an hour to figure this out. You can call me if you have any question 718 864 6960.
PS Connector 4 on the logic board is responsible for power even without video you should still be able to hear that default chargin sound when connected to a power source. The best way to be certain is to remove the cables and reattach them as the fitting are a lil cumbersome to work with