The problem is simply the viewport.
If you render the image it comes out right.
The problem has to do with the way Blender scales images to fit textures. It could scale them so a tiny pixel would look like a box, but it uses the more conventional method, which is to scale them so that they blur. (zooming in on the texture in the image viewer scales the first way though.) (Blender scales like Gimp does, which works best for most things. Put the texture in Gimp and scale to see what I mean.)
To really fix this problem, you must simply scale the texture in a program that doesn't blur it, and use the larger texture instead. I would just zoom in on the image in Blender, take a screenshot, then cut out the texture.
You then get this.
You can use that image in Blender Internal or cycles and it won't be blurry.
Keep in mind, with Blender internal, you must switch to material viewport to make the blurring go away, because the solid viewport will not show the texture correctly.
You may have to change the texture, then save and close Blender then re-open to see the change take effect in the viewport.
It should look like this now. (your background will be grey, the white is my theme).
I hope this fixes it.