Barry George, 48, had a hatred for the public broadcaster, was fascinated with weapons and frequently stalked women near Dando's Fulham home, the Old Bailey was told.
The 37-year-old "Crimewatch" presenter was gunned down in her doorway in April 1999.
Prosecutors told the jury there was no direct evidence linking George - who has a personality disorder - to the crime, but various additional strands of circumstantial evidence "provide a compelling case".
Dressed in a blue shirt, matching tie and navy trousers, George sat impassively in the dock alongside a clinical psychologist to help him as the case against him was outlined.
He was originally tried for Dando's killing in 2001 and is now facing a retrial.
George, who lived nearby, denies murdering Dando with a single gunshot to the head, five months before she was due to be married.
Opening the retrial, prosecutor Jonathan Laidlaw said Dando's murder was not a well planned execution.
"On the contrary the murder was the work of a single individual, a loner, a man acting alone, with no rational motive to kill," he told the jury.
He said Dando was universally popular, a warm, kind, generous woman, easy to work with, who had no "pretensions that are sometimes associated with those who achieve fame".
Laidlaw told the court there were several sets of circumstantial evidence, which proved George's guilt.
"He had a fixation with the famous and celebrities - for many years he lived out the fantasy by calling himself after and adopting the names of various entertainers," he said.
"He had pretended to be an SAS soldier and in the years immediately before Miss Dando's death was pretending to be Freddie Mercury's cousin."
He had lied to police about his movements on the day of the murder, changed his story during interviews and had been spotted in the vicinity at the time of the shooting.
In the lead-up to the murder, he was also seen loitering near the BBC's west London offices while at the same time developing an unhealthy fascination with female TV personalities.
The jury heard that police found more than 4,000 undeveloped pictures of various women at his home as well as a picture of him holding a gun, which prosecutors said was similar to the murder weapon.
"They raise the question - had (his) fascination with female presenters, combined with Jill Dando's link with the BBC, and his belief (the) organisation had treated Freddie Mercury badly, resulted in this irrational plan to kill," he said.
The jury were warned to ignore the widespread publicity that has surrounded the case since the 1999 murder.
The trial, before Mr Justice Griffith Williams, continues.
