If the power button llights, but no display, could be several things.
I loose lcd panel cable, or the inverter is not powering, or any number of things could result in your Lilli's problems. If you are comfortable with opening the unit, have a look and verify that all connectors are seated properly. Do this without power connected.
I doubt you experienced a voltage spike, as the led is on. If you killed it, you would not even have that.