Voltage regulator for laptop

Hi there. I have a problem for which I'd like some opinions: I have a PB laptop which has fried its inverter for the LCD due to the input voltage towards the inverter being too high (19v while it should be 12v and can only endure upto 13v). Most PB models have this problem. I looked around and some people suggest making a voltage regulator with a 7812 and some capacitors that gets its power directly from the input of the power adapter on the laptop (19v, 6+ amps). But since I am not really that into electronics, I have no idea if this will work, especially towards the heat that comes with the 7812, will it be high? The inverter needs around 0.5 amps input current. Others suggest a setup with (zener) diodes, but I have no clue how to start on that. Anybody have a suggestion? Many thanks.