It was around 2007 or 2008 I think. He still did the salute once he became the "Marine" in 2006 but his entrance was walking rather than running. If you really wanna know, it'd probably be best to check out a few random PPV matches from that period to see where it starts.
EDIT: Just checked a few of his 2008 entrances. The earlier I saw of him running is SummerSlam against Batista. So mid 2008 is probably the answer.