I haven't seen much support regarding more complex electronic control for a custom projector... so I devised one:

Hopefully you can follow the design - all the magic happens in the "Electronics Box." It is powered by a 12V adapter. The main power switch is designed to always be swtiched on (like your computer's main power switch (if it has one)). What makes this design awesome is that it is entirely controlled by the monitor's control panel (the monitor's power switch). It turns on the LCD panel, the lamp, and the fan. This design also includes a feature that keeps the fan running for a minute or more after the monitor has been turned off. The Backlight Cable from the monitor is used to tell the Electronics Box to turn on the ballast and fan. This design can also be adjusted to have a temperature-sensor to control the fan. The reason why the relay is important is so that there is one button to turn the machine on and off and still be able to keep the fan running (so you cannot simply turn off the main power switch).
Schematic diagrams of the electronics box may come soon. I still have to figure out certain properties regarding the backlight, timing for fans (or temperature-sensor alternative), and other things.
Any comments or criticism is most welcome