Barrett played high school hockey at Dimond High School in Anchorage.
Barrett played college hockey at the University of Maine. He was drafted by the Buffalo Sabres in the first round with 20th overall pick in the 1999 NHL Entry Draft. Having not been signed by the Sabres, the New York Rangers signed him as a free agent in 2001. He played just ten games with the Rangers before being traded to the Dallas Stars along with Manny Malhotra for Martin Ručínský and Roman Lyashenko. He spent the next two years playing for the Stars AHL team, the Utah Grizzlies. He was not resigned, and in 2004 signed a one year deal with New York Islanders, although he never played for them due to the lockout. In 2005, he was contemplating retirement when his brother Chris asked him to play alongside him in the ECHL for their hometown team, the Alaska Aces. He signed with the Aces and helped them win the Kelly Cup, the ECHL's championship trophy.
Heisten re-signed with the Aces heading into the 2006–07 ECHL season, and was named an alternate captain. During the summer following that season he declared retirement, but later decided to come back and hopefully enjoy a better, less injury-riddled season. He was named captain by coach Keith McCambridge. Although his numbers weren't near outstanding, He contributed valuable leadership to the team. His healthier season, however, was not to be. He suffered a concussion in a game on December 11 in which the Aces played host to the Stockton Thunder. He returned on the 19 of December in a game at Victoria, only to see the symptoms flare up again. After missing 15 consecutive games, Barrett announced retirement on January 18 in consideration of his long-term health.
|1997–98||US Jr. National Team||USHL||16||3||9||12||68||—||—||—||—||—|
|1998–99||University of Maine||HE||34||12||16||28||72||—||—||—||—||—|
|1999–00||University of Maine||HE||37||13||24||37||86||—||—||—||—||—|
|2001–02||New York Rangers||NHL||10||0||0||0||2||—||—||—||—||—|
|2001–02||Hartford Wolf Pack||AHL||49||9||9||18||60||—||—||—||—||—|
|2004–05||Bridgeport Sound Tigers||AHL||67||7||12||19||59||—||—||—||—||—|
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