Although it's not my original idea (far from it), I finally decided to tear apart my LCD monitor and give this one a go. I had to innovate a few parts, so I hope my solutions help anyone out who's attempting this awesome project. This is my first instructable, be gentle :)
Step 1: Materials and Initial Disassembly
LCD Monitor, any old one will do, the backlighting is going to be ripped out anyway. In my case, 14" was perfect, larger would have gone outside the border of the overhead's window.
Overhead projector, like from school. I'm no expert at these, and living in Taiwan, it was nearly impossible to find, but I know there are loads on ebay for cheap.
Document protector, used for housing the power and settings strip of the monitor.
Cork. Self explanatory.
First, get the LCD glass out of the monitor by carefully unscrewing, dismembering and prying. Be careful around the wires and you should be fine. One handy thing is that on mine, the display cable was detachable from the motherboard, so that made it easier. It's helpful to have a second pair of hands for this, in my case, I used my girlfriend's.
Step 2: Initial Assembly and Test
The hardest part is over. Now it's just a matter of coming up with some sort of mounting and enclosure construction. You're going to want to space the screen up from the projector window, as it gets super hot, and could damage your LCD. I used a cork, cut into four pieces and slit 50% down the middle.
I found that my projector was overheating and shutting off by itself, so I mounted a fan on the inside of the casing to get the air moving a bit.
Step 3: Casing
With all the plugging and unplugging I was doing of all the components, I felt like the power jack on the mainboard was getting a little flimsy (it's only held on by solder, I think), so I put the entire board inside a document protector, which closed pretty well with only the jack and the VGA port sticking out.
After a brilliant suggestion from Alyosha, I have since created a bellows as a variable-height enclosure. I will be posting a separate instructable for it presently.
Step 4: Finished!
Sorry about the poor quality of the picture, but I had to take this with my mobile phone. There is some light spill-off from the projector itself, I later ended up covering the sides with a black plastic bag temporarily (it needs some vertical give to adjust the focus).
I have just finished creating a bellows that serves as a wonderful variable height enclosure and keeps the light spill-off to a minimum. See step 3.
Overall, the project was pretty simple, and it works great! I'm going to be making a rear projection screen for it, which I'll post a separate instructable for as soon as I finish.