Robert, I checked your profile there is no reference to another question asked here. It seems you researched the problem and determined that the inverter was the cause - Actually a very good analogy from the information given.
Your problem could be:
1) The inverter cable.
2) The backlight CCFL bulb.
3) On the motherboard.
If you own or have access to a multimeter/multitester (An analog one with the needle, is best for testing internal breaks in wires. The digital ones have slow reaction time.) you can test the integrity of the inverter cable with a continuity test while moving the wires around. If the needle sweeps hard at any point the cable could be the cause. By doing this you can determine if this part is the problem or not. Many people would frown upon this suggestion but, you can purchase a meter such as this and return it to the store after your minute with it is done. Don't take it back just yet, we might need it for another minute to yet to test voltages.
We need to know more things about this as we don't have physical access to the machine in question. Is there a red/pink/orange hue to the screen when it is lit - "especially just prior to it going dark"? Is there any flickering to the screen - again, "especially just prior to the screen going dark"? Is there any humming noise coming from the lower part of the screen - again....." "? Has this system ever experienced any liquid damage? What country is this laptop in? Please give us the last 3 characters of your serial number so we can determine your exact machine. If there is any further information you can think to add, please do so.