It's a live ball until the runner gets hit. if a runner gets hit, it is the equivalent of getting tagged out. So the runner on third has to tag up third base if the ball is a line drive, or if its a grounder, then the runner on third should have already ran home. Then you would have either bases loaded or runners on first and second with a run scored - respectively.

Ball is dead. Play is over. Runner who was hit by the ball is out. Batter gets credited with a hit and is awarded 1st base. Runner on 1st goes to 2nd. Player at 3rd stays at third. Just to complicate things a little. If the infielders were playing in on the grass and the ball went past the shortstop and then hit the runner, the ball is live and play continues.

Although it is understandably complex, the MLB Rules do support the batter being called safe (automatically awarded 1st base, the runner going from 2nd to 3rd being called out, the runner going from 1st to 2nd being awarded 2nd base, and the runner going from 3rd to home having to return to his bases...all with a dead ball being called. To wit, consider the following two rules (5.09 & 7.04 from the Offical Rules of Major League Baseball): 5.09 The ball becomes dead and runners advance one base, or return to their bases, without liability to be put out, when— (f) A fair ball touches a runner or an umpire on fair territory before it touches an infielder including the pitcher, or touches an umpire before it has passed an infielder other than the pitcher. 7.04 Each runner, other than the batter, may without liability to be put out, advance one base when— (b) The batter’s advance without liability to be put out forces the runner to vacate his base, or when the batter hits a fair ball that touches another runner or the umpire before such ball has been touched by, or has passed a fielder, if the runner is forced to advance; Emphasis on the phrase "if the runner is forced to advance." Remember the "force" part of this. Simply put, because the runner going from 2nd to 3rd was automatically out, the runner going from 3rd to home was not forced to advance (although the runner going from 1st to 2nd was forced to advance due to the force of having the batter awarded first base). Therefore, the runner going from 3rd to home must return to his base ("without liability to be put out"). In the case of a runner being hit by a batted ball, no run could ever score because the runner on third would never be forced to advance...because a runner behind him was automatically called out and a dead ball ensued. The logic of these two rules is to protect the defense, which could not have made a play at home after the ball was deflected by the runner. The protection offered as a balance to the offense is that the other runners are not liable to be put out.