Corporal Brady was a member of Company H, 2nd Battalion, 38th Infantry Regiment, 2nd Infantry Division. He was listed as Missing in Action while fighting the enemy in South Korea on 17 May 1951. He was presumed dead on 31 December 1953. His name is inscribed on the Courts of the Missing at the Honolulu Memorial.

Brady was awarded the Purple Heart, the Combat Infantryman Badge, the Korean Service Medal, the United Nations Service Medal, the National Defense Service Medal, the Korean Presidential Unit Citation and the Republic of Korea War Service Medal.