Parnell attended Gosnell High School in Gosnell, Arkansas, where he lettered in basketball, helping his team to the state semifinals, while earning all-state honors twice and averaging a double-double during his junior and senior seasons.
He accepted a basketball scholarship to play at the University of Mississippi, where he played four years. In 2009 as a senior, although he hadn’t played football since the eighth grade, head coach Houston Nutt convinced him to try out for the team, which led him to play in five games as a defensive end.
Parnell signed with the New Orleans Saints in 2009 as an undrafted free agent to play defensive end. He was waived at the end of training camp, but spent the rest of the season on their practice squad where he was tried at defensive tackle, tight end and the offensive line. Although he was never in a game, he was awarded a Super Bowl XLIV ring. He was released by the Saints before the start of the 2010 season.
Parnell was claimed by the Miami Dolphins to their active roster, where he remained for 20 days until being released on September 25, 2010, to make room for Patrick Brown, whom the Dolphins claimed off waivers from the New York Jets.
After his release, he was signed to the New Orleans Saints' practice squad on September 29, 2010.
The Dallas Cowboys signed Parnell to their active roster on October 14, 2010 with the intention of converting him to a full-time offensive tackle. The next year, he participated in his first six career games, playing on special teams and as a backup offensive tackle.
On April 26, 2012, he was re-signed to a three-year contract. That same season after Tyron Smith suffered a high ankle sprain against the Cleveland Browns, he replaced him as the team starting left tackle and also in the next game against the Washington Redskins. When Smith returned, Parnell was worked into a regular rotation with starting right tackle Doug Free. The next year, he was expected to compete for the right tackle position with Free, but suffered a hamstring injury during the preseason and fell behind.
In 2014, he started eight games at right tackle including the playoffs, after Free was sidelined with a foot fracture and an ankle injury.
On March 11, 2015, Parnell signed with the Jacksonville Jaguars as an unrestricted free agent, to become the starter at right tackle and help to upgrade one of the worst offensive lines in the league. He started 15 games and was declared inactive in the last contest of the season because of a hamstring injury.
Parnell met his wife, Kadeshia Fortune-Parnell, in college at Mississippi. She is a teacher and a track and field coach.