if you want to hook up a projector to a computer to display video then the best solution would be to buy one from a retail store or website. you can get some models at reasonable prices.
unless you are capable of designing circuit boards, writing drivers, assembling a device which requires some measure of precision, as well as doing all that cheaper then a major manufacturer..... stick to retail.
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the only type of projector which is reasonably easy and inexpensive to build is the old type that uses transparencies on top of a lighted table with a prism mounted on an arm. those are constructable by any reasonably competent person who does some research.