Is batter still considered in the box
 

Fair ball goes inches directly in front of the plate. Batter goes to run and with one foot in the box, steps on the ball with the other. Since no foot has made contact with the ground outside the batters box before contact with the ball, is this a dead ball foul, or a batter out situation.

Just because the batter's foot isn't touching the ground directly, that has no bearing on this. The ball was in fair territory outside of the box, and that's where the batter contacted it. No different than if she had jumped up in the air while running to first and neither foot is on the ground when a batted ball bounces up and hits her.

Dead ball, batter is out.

Read ASA 8.2-F(4).
Read NFHS 8-2-6.
Read NCAA 12.2.13.

In every case, the batter-runner is out for making contact with a fair batted ball.

Now read ASA definition Foul Ball #4.
Read NFHS 2-25-1-f.
Read NCAA 11.5.1.

All of these describe a batted ball that hits the batter while still in the batter's box.

In your play, the batted ball did not hit the batter; you described the batter-runner contacting the fair batted ball. The batter's box does NOT APPLY TO THAT RULING!!

Steve, I had read the definition from my 2012 ASA book "F"- touches the batter while the batter is within the box. Since the batter had not placed a foot on the ground outside the box I was wondering if by definition she was still in the box. If you guys say she can be out of the box without contacting the ground yet ?- Okay..

Chuck,

I believe the second set of rules Steve noted is to protect the batter from a ball off the bat that is basically direct from the bat and relatively unavoidable.

In the OP, the runner caused the contact with a fair batted ball.

When it comes to batting the ball illegally, a batter whose foot is out of the batter's box but still in the air is not in violation. But this has nothing to do with the batter being in fair or foul territory. That rule penalizes the batter for batting a ball with her foot completely out of the box and on the ground. It doesn't say anything about the foot being in fair or foul territory.

So be careful comparing the status of the batter and her foot under that rule, and her status under other rules. In ASA 8-2-F-4, the batter's box isn't even mentioned. It just says a batter-runner is out when she contacts a fair ball. Heck, the ball could still be in the box but fair, and if the runner kicks it, steps on it, picks it up, etc., she would be out.