If the knee of an offensive player carrying the football never touches the ground but the players hand or arm carrying the ball does is the player down?

he can get up and run if he has not been touched yet. then he has to be tackled to be down, not "touched".

The above is true in the NFL...the touch must have caused the fall or happened while the knee or elbow is on the ground.

In college or ANY level below the play ends when the players knee or elbow touches regardless of the reason.