Martinek was an average athlete at Hopatcong High School in Hopatcong, New Jersey, playing American football and track & field but he soon came to be one of the best. As a senior running back at Hopatcong High School, Martinek was named the state's 2006 Gatorade player of the year after finishing the season with 2,081 yards rushing and a career total of 7,589 yards for the Chiefs. He became the first player in New Jersey to gain more than 7,000 yards, and at the time of graduation was ranked 38th on the all-time high school football rushing list.
Martinek was seventh in the state in scoring as a senior, with 160 points, and had the second-best single-game rushing total in New Jersey as a senior with 396 yards on 31 carries and four touchdowns vs. Jefferson High School. He garnered First Team All-State honors by the Associated Press and the Star-Ledger. He was invited to play in the NY/NJ High School All-Star Classic. Martinek also excelled on the other sides of the ball. On defense at linebacker, he recorded 54 tackles, four sacks, three interceptions and nine pass breakups. On special teams, he was 31-of-34 on field goal attempts (and 6-for-6 on attempts of 50 yards or longer) and punted 16 times with a net average of 46.6 yards. Joe appeared in the January 11, 2007 edition of Sports Illustrated in the “Faces in the Crowd” section, highlighting his New Jersey state rushing record and tremendous special teams statistics. Joe was also a standout track performer who won the state title in the javelin in 2007.
Martinek was a four-year starter at Hopatcong under head coach Paul Reduzzi. Coach Reduzzi on Martinek: “Joe is a tremendous individual and tremendous athlete. With the success we had on the field the last four years was a result of Joe helping his teammates and making them better on and off the field.”
While in high school, Martinek received an offer from Rutgers.
Martinek was redshirted his freshman season in 2007. During that first season, Joe did not see game action but helped prepare the team as a member of the scout team. He competed as both a running back and a safety during practice drills.
After his redshirt year, Martinek had a strong freshman season in 2008 with 404 yards rushing and four touchdowns. He averaged 5.3 yards per carry and was also a standout on special teams. He made his collegiate debut in season opener against Fresno State (9/1) and caught one pass for seven yards in the second half against the Bulldogs. He recorded his first career carry in the first quarter at Navy (9/20) and one play later scored a five-yard touchdown on his second career rush. He finished the game with 61 yards rushing on eight attempts, including a 29-yard run in the second quarter. Against UConn, Joe delivered a big tackle on the one-yard line on a second-half kickoff against the Huskies. Against Syracuse (11/8), Joe took the ball from the direct snap and rushed a career-long 45 yards for his second career touchdown. Against USF on 11/15, Joe posted career-highs in rushes (21), rushing yards (98) and rushing touchdowns (2) at USF. Joe had 53 yards on nine carries against Army (11/22). He made his first career start in the regular-season finale against Louisville(12/4) and rushed 18 times for 57 yards, including a 22-yarder. He carried nine times for 58 yards, including a 26-yard rush, all in the second half of the PapaJohns.com Bowl against NC State (12/29) in support of Rutgers come from behind bowl victory.
Martinek signed with the New York Giants as an undrafted free agent on April 28, 2012 and waived August 27, 2012 as NFL teams trimmed their rosters to 75. He was re-signed to their Practice Squad on October 10, 2012.
In May 2015, Martinek signed with the Parma Panthers of the Italian Football League.