i have a doubt, whether the poer supply that came along with LCD display is not low voltage AC instead of DC and it is managed inside the LCD panel.-- perhaps your LCD also warrents -ve voltage? and when you think of extending the 12DC there, it may not abe able too produce _ve voltages.--
this case may perhaps be comparable to external modems of yesterdays, with used to come with a step down transformer.
Having said all this may i ask for make and model number of the LCD display device that you bought?
Sarma