The first attempt ended in a mistrial after a lawmaker suggested the still-deliberating jury had acquitted one of the suspects.
On Wednesday, one of the defendants, ambulance driver Tarino Lightbourne, told a judge he had no money to hire an attorney for the proceedings and pleaded with the public to help him financially.
His previous lawyer said he cannot afford to represent his client pro bono again and asked the judge if the court would pay him a stipend. Supreme Court Judge Jon Isaacs said he would consider the request.
Lighbourne and former Sen. Pleasant Bridgewater are accused of threatening to sell stories to the media about the death of 16-year-old Jett unless they were paid $25 million.
Bridgewater's attorney, Murrio Ducille, told reporters that there is no case against his client and that he would not change his defense strategy. He previously accused Travolta's attorney of setting up his client by meeting at a hotel room where Bahamas police had installed hidden cameras.
Prosecutors say the two defendants agreed to accept $10 million in installments over a four-year period before they were arrested.
In October, a judge ordered a new trial after a lawmaker suggested the still-deliberating jury had acquitted one of the defendants. Legislator Picewell Forbes said Bridgewater was "a free woman" during a televised speech.
He declined to say who gave him the information, and one of his lawyers had said he was just repeating a rumor.
Jurors had heard a month of testimony from witnesses, including Travolta, who revealed publicly for the first time that his son was autistic. Jett died Jan. 2 after suffering a seizure at his family's vacation home in Grand Bahama.
It is unclear whether Travolta will testify again. A publicist did not immediately return a call for comment.