No video but has sound

Take a flashlight and point it at the screen. If you can see a subdued dark image, then it is the backlight. It is usually not the actual backlight that is out, but the backlight power inverter, which can be replaced. Google or go to Utube and find backlight power inverter replacement. There are many sources and quite a few videos on how to accomplish this. It is probably not the power supply, as the TV turns on and has audio. Most of the newest sets are composed of only 3 circuit boards. One being the power supply. If you cannot see anything with a bright light source pointed at the screen, but still have audio, I would look up the other boards and see if an inexpensive replacement is available.

This is a start. You may or may not be successful using this information, but I have fixed more than one TV and quite a few monitors just replacing the inverter.