It's pretty black and white: no.
Almost every country in the world has joined the Berne Convention, and has copyright terms meeting the minimum standards of that convention (at least 50 years after the death of the author). Presumably, these textures are the original ones created by Markus Persson, so various special rules such as the US's 95 years for corporate authorship don't apply. In that case, the clock on the copyright term hasn't started ticking yet.
Modifying the textures won't help, either: this is called creating a derivative work. Most countries permit creating derivative works for certain purposes (such as commenting on the original work), but this won't help in your case. Your derivative work would be used as a reasonably direct competitor for Minecraft, which isn't permitted under any country's copyright law.
Copyright isn't a "use it or lose it" situation like trademark, either. The fact that these textures are unused in the current version of Minecraft has no bearing on their copyright status.
Independent creation is fine (copyright is about copying, after all), but you need to be sure your creation is independent -- you can't just bring up a Minecraft texture as a reference and draw something that looks like it. The safest option would be to find an artist to draw textures for you, and provide written descriptions of what you need (eg. "a tileable 32x32 pixel-graphics texture of a cross-section through dirt").