'''Anthony Gonzalez''' this sounds like a cold solder joint or a failed capacitor on your power board. Let us know what the exact model of your TV is. Remove the back of your TV and look at all the boards for obviously damaged components as well as loose wires etc. Post some images of your boards with your question so that we can see what you see. Use this guide Adding images to an existing question for that.
Anthony Gonzalez "first turned on the power supply does not have enough power built" not quite. I think what happens is that components heat up and then close a gap like a cold solder joint. As it heats up the gap closes and now the circuit works. I have seen that before with failed capacitors. Always remember that just because a capacitor looks good, it may still have failed. "I see an image so I don’t know if is the main board" means that your mainboard and T-con board are producing what they are intended to do but the backlight is not. That is why I consider the power supply and then the inverter. Going by your measurements, when the backlight is either in the on or off state, leads me to believe that this is a power board issue. I’d be checking diode DM855 and DM854 BTW, great job documenting your measurements.
Here is the schematic for your power board <443A5CBEF7B9ABB0FCB7C35C28C0FAB0A1C7FC294856333248445F3944595CBDC2C0CEBFF820B0FCB7C32E2E2E>
Those are Schottky Diodes and they are part of your rectifier circuit. Very simply put they convert AC to DC. Here are the datasheets for both of those. FMEN-210AFMEN-220A Use this information to test them. Consider each on as two diodes. So test left and center pin as one and the right and center pin as the other