The screen requires two types of power...
It first needs 3.3 or 5V for the control board (goes in through the cable with all of the red/green/blue)
It also needs High AC voltage for the backlight. Your inverter should have a 5V or 12V in and then a ~500V AC out. You need to give it the power it needs, and hook the high voltage ac up to the backlight. This should be a completely seperate plug from the rest of it.
Hooking up the inverter to the control board input would produce a great pyrotechnic show, however (*BOOOM* )