I would certainly try a new digitizer to see if that helps. In the meantime, disconnect the digitizer and LCD (disconnect the battery first!) and then connect the iPad to an iTunes enabled computer to see if it boots and is recognized. If it is, then add the LCD first (again…disconnect the battery first!) and test again. If it works, then try to add the digitizer. This should help you identify the bad part if that is the problem.
If the device boots and is recognized but you can’t see anything on the screen, the you need to determine if the backlight and LCD driver circuits are working properly. Try shining a bright light on the screen to see if there is a dim image or not.
If the iPad doesn’t boot with no LCD or digitizer, then you may have a deeper logic board issue.