He presumably commanded U.S. forces during the defense of Washington D.C. After the EMP, he gathered some of the stranded U.S. soldiers to assault Whiskey Hotel to prevent friendly airstrikes that were planned for Washington, D.C. He is first mentioned by Pvt. Vaughan in "Second Sun". He is seen informing Sgt. Foley's squad about the new objective: take back the White House. He is then seen in the level "Whiskey Hotel" when Foley's squad emerges from the President's bunker, providing them with new orders and observing the battle from afar. He presumably survives the battle, as they are successful in retaking Washington D.C.
Apart from Shepherd, Marshall has the highest rank out of any of the characters in the game.
Colonel Marshall's name is not abbreviated in subtitles but is abbreviated when the player points their crosshairs at him.
If you go back to his position after a while and when the bombing run timer starts, you will see that all soldiers are K.I.A., except Marshall, a Lieutenant spotting with binoculars, and another randomly generated soldier.
Strangly, Marshall is able to tell that Foley is a Sergeant, with barely a glance at him. It is possible that Marshall assumed Foley was a Sergeant, since Foley was the first (and only) one from the squad to go up and talk to him.
It is possible that he commands the 75th Ranger Regiment, as Colonels lead Regiments, and he was the highest-ranking officer at the battle to retake Whiskey Hotel.
Before and after being talked to, Colonel Marshall will have a static, immovable model.