You can make an LCD projector with an old LCD monitor, an overhead projector and a light source (or just a fresnel lens and a focusing lens, available online with a quick search). LEDs with enough power to light an LCD projector are expensive- think hundreds of dollars. Metal halide lamps are much cheaper, and easier to work with, but bulkier. Making an LCD projector the size of a commercial one is going to be incredibly fiddly, difficult, and potentially more expensive than just buying a projector. The smallest DIY ones I've seen are boxes about 1 x 1 x 2 feet.