OK, I have assembled the TV. I have also found a broken trace on the main board, and repaired it.
Now, when I turn on the TV, there is still nothing on the screen (no antenna, so it should show "snow"/static).
But, the difference from before is that now the LED screen (that shows what TV channel is selected) works, and when I change the channels it shows that. Also, when I turn off the TV, now there is no white square that shrinks into a dot, and there is no loud sound of vacuum. Now it sounds normally when turned off. Remote control works.
But the screen is actually OFF. It remains completely the same whether the TV in on or off. :/
Also, there is some cracking heard from the speaker.