Michael Menson was discovered lying fatally injured on the North Circular road in Edmonton, north London, early on 28 January last year.
The police made extensive inquiries but are unclear whether he was killed or if Mr Menson, a registered schizophrenic, set himself on fire, Hornsey coroner's court was told.
Detective Chief Inspector Robert Scott said Mr Menson's brother Kwesi had insisted that the musician, who had five hit singles in the 1980s with the group Double Trouble, had told him from his hospital bed that he had been attacked by four youths.
Det Ch Insp Scott said Kwesi had insisted: "Michael made mention of four youths on a bus and they might be responsible."
His officers had spoken to about 300 people, including one now living in northern Cyprus, about the death. They had also taken up to 200 statements.
"Not one witness of any substance has been found in the last 18 months that can give us any concrete facts about how this happened," he said. However, the death was being treated as murder.
Mr Menson, the son of a Ghanaian diplomat, died in Billericay hospital, Essex, in February from his injuries.
Rajiv Sharma, consultant psychiatrist, who was treating him at Chase Farm Hospital at the time of the incident, told the inquest that Mr Menson was a schizophrenic who suffered bouts of acute psychosis including hallucinations and delusional beliefs that he was being followed and persecuted.
Mr Menson may have harboured suicidal ideas, Dr Sharma said, but he did not have the necessary "suicidal intent".
When Dr Sharma last saw Mr Menson as an outpatient on 10 January, the musician's "mood was good".
Brian Leslie, who saw the burning man, said Mr Menson failed to react to the fact that he was on fire. Initially Mr Menson was "strolling" and "relaxed" despite the fact that his back was on fire, Mr Leslie added.
Constable Johanna Walsh, the first police officer on the scene, said Mr Menson, who appeared to be "in a trance", had left a trail of burning clothes along the road. She asked him three times who had done that to him and received no response. The fourth time Mr Menson replied simply "Lee".
He responded positively when she asked him if that was someone he knew. Nevertheless, Ms Walsh said, it was not necessary to cordon off the area as a crime scene because she believed Mr Menson had set himself alight.
Terry Munyard, counsel for Mr Menson's family, asked the PC why she had disregarded the injured man's apparent claim that someone else had set him on fire.
She said: "I didn't at the time believe that he knew what he was saying."
The inquest continues.