Fast-pitch softball

Question
Bases loaded, bottom of the 7th innning.  Batter is hit by pitch.  Does not go to first base, she goes toward first, stops at dugout to celebrate with teammates.  Has not touched first, nor does.  Is the game over? Is the batter out? Does the run from third count.  Score is tied and 1 out.  

Answer
Mike,

A bit of delay in answering this questions.   You state that the batter doesn't touch first and doesn't ever complete their duty to go to first base.  At first glance it seemed easy.  Batter out for leaving the playing area when they stepped into the dugout.  This is what you would have if the ball was live.  But the ball wasn't live.  Hit by pitch is a dead ball.  I couldn't think of a way to call an out when the ball is dead.  Next step was to check the rule book.

2010 NFHS Rule book 8-2.4

The batter-runner shall be declared out when:

The batter runner fails to advance to first base and enters the team area after a batted fair ball, a base on balls, a hit batter (F.P.)a dropped third strike (F.P.), or catcher obstruction.
     EXCEPTION:  (S.P.) The ball is dead on a base on balls, or on a hit batter (F.P.) the ball is dead, the batter runner is not out and runners can not advance unless forced.

The way I read this, is the batter is not out for leaving the field because the ball is dead.  The runners can't advance unless forced.  The coach needs to make sure the batter goes back on the field to touch first base and the runner on third needs to touch home.  Only then is the game over.

Tom