When changing your screen, did you change the touch pad? and have you managed to open your phone any other time after changing the screen?
There might be two explanations; either your new screen is not compatible with the touch pad or your touch pad isn't working properly. I am also concerned whether the person who was changing your screen tested whether its working properly. Try getting the touch pad changed too and see how that works for you, its not your phone, its one of the two; screen or touch pad.