Parnell attended Gosnell High School in Gosnell, Arkansas, where he lettered in basketball. As a senior, he registered averages of 21 points, 13 rebounds, 5 assists and 4 blocks, contributing to his team reaching the 2004 3A State Tournament semifinals. He earned All-state honors twice, while averaging a double-double during his junior and senior seasons. He accepted a basketball scholarship from the University of Mississippi. As a junior, he averaged 4.9 point and 4.0 rebounds per contest. As a senior, he started 7 out of 30 games, averaging 3.7 points and 3.3 rebounds per contest, while ranking second on the team with 22 blocked shots. As a senior in 2009, although he hadn’t played football since the eighth grade, head coachHouston Nutt convinced him to try out for the football team, which led him to play in five games as a defensive end and make one tackle for a loss.
On September 5, 2010, Parnell was claimed by the Miami Dolphins to their active roster, where he remained for 20 days until being released on September 25, to make room for Patrick Brown, whom the Dolphins claimed off waivers from the New York Jets.
New Orleans Saints (second stint)
On September 29, 2010, he was signed to the New Orleans Saints' practice squad.
Dallas Cowboys
On October 14, 2010, the Dallas Cowboys signed Parnell to their active roster with the intention of converting him to a full-time offensive tackle. In 2011, 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 tackleDoug Free. In 2013, 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.
Jacksonville Jaguars
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 started all 16 games in 2016. He started 13 games, missing three contests with a knee injury in 2017. In 2018, Parnell started the first 13 games at right tackle, before being placed on injured reserve with a knee injury on December 22. On March 9, 2019, Parnell was released by the Jaguars. He started at right tackle in all the 57 games he played in, missing 7 contests with injury problems.
Personal life
Parnell met his wife, Kadeshia Fortune-Parnell, in college at the University of Mississippi. She is a teacher and a track and field coach.