This is what most common CCFL-LCD with inverter attached looks like (screen with Cold Cathode Fluorescent Light backlight).

Connection "A" - screen receives video signal from the video card cable.
Connection "B" - socket for backlight cable of inverter (not all laptops have it, in most cases there is just the cable by itself).
Connection "C" - power connection for the inverter.

Two most common screen issues:
1. Issues with backlight.
2. Issues with the video signal.

Issues with the video signal may be caused by the video card, motherboard, cable, defective screen, etc. In these cases screen lights up, but the image is corrupt. ATTENTION! Before installing the screen it is necessary to remove the battery from the laptop and disconnect it from the adapter in order to reset the video card for it to recognize your new screen. Skipping this step may cause issues with the video signal.

Problems with the backlight may be caused by the incomplete or improper installation, defective inverter, fluorescent tube or lack of power from the motherboard to the inverter.

How to test the backlight:

Plug the connection "B" to the inverter. Connection "C" must be connected to the video card. Connection "A" must remain unconnected.
Turn the laptop on. If backlight is functioning, you will see white screen (as shown on the picture below).
If white screen does not appear, it may be due to one of these reasons:
- inverter does not receive enough power from the motherboard
- defective or damaged video cable
- defective or damaged inverter
- broken fluorescent backlight tube
Also, you may find this article helpful.

Please see pictures below for more examples on what typical issues caused by motherboard (video card), cables, incomplete connection, etc. look like. If your screen issue looks similar, do not jump to conclusions, because only a professional diagnostic may help you determine the cause.