My new iPhone 4 display does not work.

If the display does not show anything or the touch does not react, one of the data cables might be damaged. These cables are very delicate and can be creased or ripped easily during installation. 

Do they have any kink, rip or surface damage? 

Most of the time the digitizer cable is not thread through all the way and appears to be too short. Pulling it will make it tear on the other side. In rare cases, if the screen does not show anything, the data cable is broken near the display. 

We are happy to help you if you contact us by providing your order number. Some photos of the cables and the screen in action might help analyze the problem.