After you've ruled out needs hard reset, bad LCD (try with your old cracked one), and no power (iTunes will detect), then you are looking at backlight problem.
Most of the time in your situation, you have a refurbished screen where the small piece of tape that should cover the backlight flex on the new screen has come off. When you did your final install of the new screen, the open solder connections on the backlight flex will touch ground metal of the frame and this will burn a backlight filter on the board near the LCD connector. If you pull the sticker around the LCD connector, you may be able to see the burned filter---this is the component that needs to be replaced.
No it is not easy as DIY unless you have experience with microsoldering. However, in the hands of a microsolderer, it is very straightforward to work with these tiny clearances using the right equipment. If you need a professional, you may follow the link to my iFixit Pro profile, iPad Rehab.
Jessa