Suggest you replace the Inverter. A Backlight goes out all at once.
90% of the time the Inverter is the hardware part at fault.
[ An LCD screen cannot produce enough light by itself.
A Backlight is used to supply the needed extra lighting.
A Backlight is a CCFL.
Cold Cathode Fluorescent Lamp.
Similar to Fluorescent lighting used in homes, and businesses, but on a much smaller scale
An Inverter is used to required power for the LCD screen, and the Backlight.
Boosts power up for the LCD screen, brings it down for the Backlight.
Dell Support > Latitude D600 Notebook PC > Service Manualhttp://support.dell.com/support/edocs/systems/latd600/en/sm/index.htm
Replacing an Inverter is a simple job. Replacing a Backlight is not.
The Backlight is located within the LCD screen assembly.
The metal frame of the LCD screen assembly is removed along the edge where the Backlight is located, to access replacing the Backlight.
In the above list for Service Manual, click on > Display Assembly and Display Latch.
This information shows you where the Inverter is located on a Dell Latitude D620 Notebook PC.
The Latitude D620 is part of the Latitude D600 series of Notebook PC's.http://www.insidemylaptop.com/remove-replace-lcd-screen-dell-latitude-d620-laptop/
Just one place from a quick search, that sells Inverters for a Latitude D600 series Notebook PC,http://www.parts-people.com/index.php?action=item&id=2895
MATCH the part number listed that they have, to the part number on your Inverter.
You have to have THE correct Inverter.