Also killed were passengers Chris Baker, 29, of Studio City, Calif., and Charles Still, 25, of Los Angeles, The Associated Press reported.
Barker, 32, and Goldstein, 35, managed to get out of the plane on their own before rescue crews arrived, according to Lynne Douglas, a spokeswoman for the Columbia Metropolitan Airport.
The four victims who died never emerged from the plane's burning wreckage.
Barker and Goldstein both suffered severe burns, and are being treated at the Joseph M. Still Burn Center in Augusta, Ga., burn center spokeswoman Beth Fritz told ABC News.
The pair had been in Columbia performing together as TRV$DJ-AM at a free concert sponsored by T-Mobile in the Five Points area. Other performers included Gavin DeGraw and Perry Farrell, frontman of Jane's Addiction and founder of Lollapalooza.
Farrell's manager, Peter Katsis, confirmed to ABC News that Farrell was not on the Learjet that crashed.
Investigators from the National Transportation Safety Board were on the scene today, trying to determine a cause of the crash. The runway where the crash occurred was closed so investigators could comb it for evidence, but they were also looking back over the past three days.
"We are very thorough," NTSB investigator Debbie Hersman said. We generally look back 72 hours at what the crew was doing, determine their work-rest schedules, their experience, whether or not their certificates are valid, their medical history.
"We are looking at everything," she said. "We have ruled nothing out."
The Learjet was taking off from the airport shortly before midnight, the Federal Aviation Administration said. Controllers in the tower saw sparks as the plane was heading down the runway, and the pilot told controllers they were going off the end of the runway.
The plane, which was heading from Columbia to Van Nuys, Calif., ran off the runway onto a local road and caught on fire. "We're looking for tire marks, we're looking for rubber, we're looking for the position of the control surfaces on the airplane," Heisman said. "We're going to be documenting all of that today."
Barker's marriage to former Miss USA Shanna Moakler was featured on an MTV reality show called "Meet the Barkers." The two, who have two children together, son Landon and daughter Alabama, are divorced.
After seven years with Blink-182, Barker started a new band, (+44), in 2005.
Goldstein is a top Hollywood DJ and co-owner of the popular club LAX who was formerly engaged to model and actress Nicole Richie. Struggles with his weight led him to undergo gastric bypass surgery. A devotee of sneaker culture, Goldstein owns a pair of Nike sneakers made especially for him.
Goldstein and Barker recently collaborated on a project called "Fix Your Face." The two performed together at the 2008 MTV Video Music Awards, where the versatile Barker was the drummer for all acts to take the stage, ranging from rock to hip-hop.
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