Any way to test a Hitachi LE55A6R9A to find why no sound or picture?

First, test fuse if there is one. Second check high voltage near 390 to 400 DC volts at the capacitor. Hopefully, there is only one capacitor.. The high voltage circuit is near where the AC 120 volts plug enters the TV. So, without high voltage, TVs are shutdown. Today's TVs are like computers, sensors on the circuit boards, feed back to a "CPU".