A group of film-makers hopes to get to the bottom of the mystery today by digging up the concrete-covered site in search of up to a million discarded copies of ET The Extraterrestrial that the game's maker wanted to hide forever.
The game and its contribution to the demise of Atari have been the source of fascination for video game enthusiasts for 30 years and the search for the cartridges will be featured in an upcoming documentary about the biggest video game company of the early 1980s.
"Bottom line, this is just trash. But there is a legend in it, we want to unlock that legend, that mystery," said a spokeswoman for the public relations firm working on behalf of Xbox Entertainment Studios, one of the companies developing the film. The documentary is expected to be released later this year on Microsoft's Xbox game consoles.
The event is expected to draw hundreds of video game enthusiasts, pop culture fans and self-described geeks to Alamogordo, a small town in south-eastern New Mexico that is home to an air force base and White Sands National Monument.
A pre-dig party took place with Atari games and free T-shirts for the first 250 people at the site.
Whether - and most importantly, why - Atari decided to bury thousands or millions of copies of the failed game is part of the urban legend and much speculation on internet blog posts and forums.
Kristen Keller, a spokeswoman at Atari, said "nobody here has any idea what that's about", and the company had no "corporate knowledge" about the Alamogordo burial.
Atari has changed hands many times over the years, and Ms Keller said: "We're just watching like everybody else." Atari currently manages about 200 classic titles such as Centipede and Asteroids. It was sold to a French company by Hasbro in 2001.
A New York Times article from September 28 1983 says 14 truckloads of discarded game cartridges and computer equipment were dumped on the site. An Atari spokesman quoted in the story said the games came from its plant in El Paso, Texas, 80 miles south of Alamogordo.
Local news reports from the time said that the landfill employees were throwing cartridges there and running a bulldozer over them before covering them with dirt and rubbish.
The city of Alamogordo agreed to give the documentarians 250 cartridges or 10% of the cartridges found, whichever is greater, according to reports.
The ET game is among the factors blamed for the decline of Atari and the collapse in the US of a multi-million dollar video game industry that did not bounce back for several years.
Tina Amini, deputy editor at gaming website Kotaku, says the game tanked because "it was practically broken". A recurring flaw, she said, was that the character of the game, the beloved extraterrestrial, would fall into traps that were almost impossible to escape and would appear constantly and unpredictably.
The company produced millions of cartridges, and although sales were not initially bad, the frustrating gameplay prompted an immense amount of returns. "They had produced so many cartridges that were unsold that even if the game was insanely successful I doubt they'd be able to keep up," Ms Amini said.
Joe Lewandowski, who became manager of the 300-acre landfill a few months after the cartridge dump and has been a consultant for the documentarians,said they used old photographs and dug exploratory wells to find the actual burial site.
A spokeswoman for Xbox said the upper layers of rubbish had been removed in preparation for the dig.
Mr Lewandowski says he remembers how the cartridge dump was a monstrous fiasco for Atari, at least from the perspective of a small desert town. The company, he says, brought truckloads from El Paso, where at the time scavenging was allowed in the city's landfills.
"Here, they didn't allow scavenging. It was a small landfill, it had a guard," he said.
The guard, however, was either away or unable to stop scores of teenagers from rummaging through the Atari waste and arriving in town trying to sell the discarded products and equipment from the backs of pick-up trucks, Mr Lewandowski, said. "That's when they decided to pour concrete over."