The concept of decimal computers actually isn't new; check out http://en.wikipedia.org/wiki/Decimal_computer
I'm not sure there would be a huge improvement in speed, though. Binary circuits are ideal; the simplicity of on vs. off is what makes them so fast and reliable (and cheap), plus it's straightforward enough to convert to and from decimal (or even emulate decimal arithmetic directly).

I think I've heard of the color-changing wall idea, but don't remember where. I think it involved some kind of OLED coating or something. I'm not sure what you mean by projector-based; all projectors I know of still use pixels. A vector-based display system using shapes instead of pixels might be possible; there were videogame arcade machines made that used that concept. It's just a different way of doing things; whether it's easy or hard depends on what you're actually trying to draw. If you wanted to display a video or bitmap image, though, you'd still have to deal with pixels.

What I mean by projector based is instead of converting from a pixel based computer to a projector, you program directly to the projector.

The projector idea seems more like you want a non-discrete display which would be cool. I've personally thought of how cool it would be to make a screen that instead of plotting pixels, it would plot basic geometric shapes.

Yeah, that would be like those vector-based CRTs in certain old videogames. I once saw a TV program that used lasers to project color vector images (even some true 3-D systems were proposed). The drawback then was that the complexity of images was limited due of the time it took to scan all the different points of the image. But if you had a system fast enough to scan a raster, you could support vector and bitmapped displays. If it was really, really fast, you might be able to directly render scalable fonts which would be awesome for reading.