First of all, Thank you so much Hitech, I really appreciate the fast answer and your detailed instructions.
Unfortunetly, the transistor temperature is near ambient, and doesn't change before or during the "blackout"
My TFT monitor is an old Compaq 1501, bought in 2003. I prefer not to buy another one, due lack of money, and because it's adapted to a custom case.
I see in your picture the PCB with two transformers. Mine only has one, and in the other side (where the second transformer would be placed) there is a set of SMT IC's.
I have identified two sets of high voltage wires coming out from the PCB, each one connected to its respective lamp. Turning on one lamp and shutting off the other doesn't prevent the blackout to occur on the operating lamp.
Since I readed your message the screen didn't turn off, but it will eventually
Please, Do you have any other suggestion?