I recently replaced the inverter on my 4 year old HP Pavilion laptop. The inverter is also informally known as a backlight. I went to HP's parts listing on their website and ordered the inverter for $30 + $10 shipping. From what I saw, the price range for an inverter is $30 - $120. The inverter is the power supply source for the background light in the LCD panel. Sometimes the screen will randomly go black yet whatever is on the screen can still barely be seen if you shine a strong external light on the panel. The inverter was located at the bottom of my laptop's LCD panel. I had to remove the panel just above the keyboard and unscrew and remove the plastic frame around the LCD panel, disconnect the old inverter, connect the new inverter, and then replace the plastic frame. The hardest part of this procedure was to convince myself I needed to remove the plastic frame containing the LCD panel. Peeling off the frame and destroying the seal provided an uneasy feeling but I was reassured when I found the inverter underneath the panel.
It is best just to replace the inverter, replacing the panel will not provide you with a new inverter, only a new panel. Go to your laptop manufacturer's webpage and see if they sell replacement parts. Look through the parts available for your laptop, find the inverter, and order it. If you are not sure, then post your laptop manufacturer name and model number so someone here can find the part for you.
Replacing the inverter is a simple, easy, and inexpensive repair that you can easily do yourself. It would be a good idea to find the manufacturer's repair manual for your laptop from the support section of your laptop manufacturer's website.
EDIT: for a temporary fix, try shutting the laptop down and disconnecting all external devices, including the power supply, mouse, network cable, and anything else that is attached to the laptop. Then reboot the laptop and it may shine brightly again until the inverter quits again.
EDIT2: Your product support page is here:
Gateway 450SX4
It appears you can easily remove that panel just above the keyboard by:
1) removing the screw on each hinge cover from the back,
2) then open the LCD panel up all the way until it is flat away from the keyboard,
3) then pry open the plastic panel with a small screwdriver. You will feel plastic notches give way. Hopefully none will break, I am not familiar with this model.
Then remove the LCD panel cover by removing the covers over the embedded screws. I assume there are four of them with one at each corner.
Peel the cover away.
At middle bottom of the LCD panel, there will be a small circuit card with some coiled copper wire and one wire connecting to the keyboard area and the other wire connecting to the LCD panel. That is the inverter, disconnect it at both ends, unscrew it from its support, remove, and replace.
EDIT3: I attempted to find the inverter amongst the components and other leads I could find but I was unable to find the inverter. You have two options if the inverter is unable to be found on the support pages. They are:
1) contact Gateway customer support and ask them how you may order the inverter for your model laptop.
2) find the serial/model numbers on the inverter within your laptop and search for these numbers on the internet to see if anyone else sells them.