If you're looking for a cheap projector (yes cheap, not just inexpensive) then the Torpedo Entertainment Projector is exactly what you've been looking for.
The Torpedo Entertainment Projector has an abysmal resolution of 940 x 240 which can almost be compared with some cell phones. Well, not quite, but you get the idea. It will project an image from many devices that is 6-feet tall.
For $169 it would be just fine for your child's cartoons, but probably not much else. Then again, it would be tempting to see how some games look on it for that price.
The Torpedo Projector: You know, for kids [via crunchgear]