In 1977, Dickerson transferred to Southern Methodist University where he was named co-captain and a starter at linebacker, finishing with 136 tackles (62 solo), one safety, one caused fumble, and one blocked kick.
After being cut by the Calgary Stampeders, he moved to Los Angeles and got a job as a maintenance department stock clerk at the Burbank Airport.
In 1979, he returned to Texas and was taking business courses at the University of Houston, when the Dallas Cowboys signed him as an undrafted free agent in 1980.
As a rookie, he contributed on special teams and in the nickel defense, replacing weakside linebacker D. D. Lewis on passing downs.
In the playoffs, he recovered a fumble against the Atlanta Falcons that set up the Cowboys' first touchdown and he intercepted a pass against the Philadelphia Eagles in the NFC title game.
His first half fumble recovery was a key play in the team's division title clinching 21–10 win over the Philadelphia Eagles.
In 1982, he remained a regular player on passing downs because of his ability to cover running backs, tallying 33 tackles, 2.5 sacks and one interception.
Dickerson entered the 1984 season as a rising star, but the team decided to alternate him with first round draft choice Billy Cannon Jr.