The LCD's have power supplies either in them or as part of the DC power cable (for the lilliput). The LCD's power supplies turn your car's
unregulated 12V DC into the regulated voltages it needs, regulated +12V.
Computers need power supplies too. But until a few years ago, your only choice was an AC in power supply that among other things provided regulated +12V and +5V DC output to the motherboard and all of the other components that plug in with those white 4 wire molex connectors. Since your computer's parts need regulated power, you can't just plug it into the car's 12Volt system, and besides, what about the 5 Volts?
In short: Yes, you do need either an inverter and AC power supply, or a DC-DC power supply. I'm sure this stuff is in the FAQ somewhere, but it's not like I'm killing trees, I guess.
