Does holding the power button while the iPad is powered on show a slide to power off screen?
I had this issue before where trying to get the iPad to display would only show backlight but no image, I fixed that before on an iPad 2 by triple clicking the home button. It seemed that assistive touch was causing a bug where screen would only display black.
Other things to rule out if you have spare replacement parts is trying another replacement digitizer and having the home button unplugged and see if the issue still persists.