You say it won't "turn on". Have you tried connecting it to iTunes to see if it is recognized?
Couple of things to look for:
- Go back through this guide and double check to insure you didn't forget anything. Always disconnect the battery first and keep track of your screws.
- Visually inspect, preferably with magnification, the connectors for the LCD, Digitizer, battery etc to see if there is any damage or debris.
- The FPC connectors are easily damaged but when they connect properly, there should be a satisfying "snap".
- If iTunes recognizes the phone, you may have a problem with the backlight or the backlight circuit. this could be caused by a defective replacement screen, connection issues or not disconnecting the battery.
- Try to put back the original screen If that one works, even though it is cracked, then your problem is with the replacement screen.