For something meant to be totally different from the originals, it looks pretty much like the same thing as Sonic 2 to me. I mean, trying to use his arms from the walking animation doesn't really works well for a punch, and the only difference I can see in the sprite style is that he has not brightening on his head (which makes him arguably worse). Maybe you should try making custom animations for his attacks, rather than just editing and putting parts together.

Also, none of the running sprites are showing up.

Also, if you still want to try going for something different, I recommend you experiment more with the sprite design and see what changes you can make to it that can still look appealing, if not just starting on a new sprite design from scratch for Sonic. Personally, I'd make Sonic's sprites in a bigger size and style (like Marvel vs Capcom or CvS) to fit in along most of the other fighters you see in Mugen, but that's just me.

That doesn't looks bad. I take it that it's supposed to be a Hadouken? But still, I personally think that his legs on the second frame of the animation could transition more properly into the Hadouken position-- as in, have the the shoes to halfway raise into the position of the Hadouken pose. Another thing I recommend is that you change his hands to look more properly positioned into how Ryu keeps his hands open, just to look more accurate:



Also, since you're basing this on the Sonic 2 sprite style, you might want to give Sonic's head the brightening that the official Sonic 2 sprites have. That way, it will stay consistent and it could also come in handy for whoever wants to use your sprites for any project.

The Hadouken in Sonic Chaos is pretty much just Sonic's pushing sprite, though, so yeah.

And also, the Sonic 1/CD sprites still had brightening in them, and besides, there is nothing stopping you from editing the sprites from Sonic 1 to be in the Sonic 2 sprite style, which requires nothing more than touching up the brightening and maybe make some areas smoother.