it COULD be modified to run off of 12 volts... it's a bit of an undertaking and involves gutting the existing power supply and installing a DC-DC convertor and possibly replacing the backlight inverter.
it is possible...not particularly practical though.
I have a relay powered by 12 volts coming from my computer's power supply to switch the AC power on a 32" LCD display. it goes on and off with my computer. Made it out of junk parts so it was basically free.