Our company buys back broken LCDs assemblies and phones from repair shops. We've been through thousands of iPhones with this issue.
My gut feeling is you have about a 75% chance that it's a bad LCD digitizer assembly and a 25% chance that the connector on the board is bad or other board related problem.
Humm... actually thinking, you wouldn't want to try the screen first. You say it wont power on. First thing is to make sure the battery connector is still connected to the board. You can see this fairly easily by removing the back cover (but be careful and read how to do so first)
For "free" you should check that and maybe it will cut on and just have a cracked screen.
Does the phone make any sound or show any signs of life? Anything show up when you plug the charger into the phone?
...if no signs of life (sound, vibrate etc, assuming that the phone has enough battery to juice up) ...you probably have an issue non related to the broken LCD screen but could have both.
If you have it charged or can charge and can feel vibrate when you hit the switch or head sounds or calls with no display, then it's the LCD.