I have a 40" H D-flat screen and it's almost impossible to get it to turn on but once in a great while when it does turn on it plays beautifully and tell it gets turned off in the process starts all over again the only thing that I found wrong with the TV is the cable plug for the back got bent sideways a little bit but still seems to work when the tv is on
Could be a power board, or system board issue. Often some capacitor burns out and needs to be replaced. You need to weight the cost of getting the board replaced vs just replacing the TV. A 40" class TV is pretty cheap, especially if you pick up a used one.