Martin was born in Saginaw, Michigan on December 30, 1977 to Lydia Moore, a single mother of two. Shortly after, the family moved south to the Oak Cliff neighborhood of Dallas, where she worked two jobs.

Later, Kenyon was often watched by his sister while their mother worked.

He was named to the NBA All-Rookie First Team and finished second in voting for NBA Rookie of the Year.

In his second season, Martin averaged 14.9 points, 5.3 rebounds, 1.3 steals and 1.7 blocks per game in helping the Nets rise from last place in the Atlantic Division to an Eastern Conference title and the best season to date in the Nets' NBA history.

He was homesick early in his freshman year and actually took a bus back to Dallas.

But his mother as well as his older sister, who by then was working two jobs and attending college, steered him to return to school.

He stuttered as a child, and attended three high schools in four years, but he sought refuge in sports, playing basketball, baseball, and football.

In high school, many major universities showed interest in his basketball prowess, but the University of Cincinnati and assistant coach John Loyer recruited him hardest after seeing him play AAU ball after his junior year.

Martin played in 70 games during the 2004–05 season, averaging 15.5 points and 7.3 rebounds; however, a problem with his knee was detected shortly into the off-season, and on May 16, 2005, Kenyon underwent microfracture surgery on his left knee.

During the 2005–06 season, Martin missed 26 games due to knee tendinitis, but was able to return in time for the playoffs.

The next year, Martin averaged 16.7 points, 9.5 rebounds and 1.3 blocks en route to his first NBA All-Star selection, as a backup forward for the Eastern Conference All-Stars.