Seth Rich was shot and killed July 10, 2016, near his home in the Bloomingdale neighborhood of Washington. (Democratic National Committee/Democratic National Committee)

When Seth Rich’s Gmail account received an alert this week from Mega.com, attempting to start a new account on a website created by the New Zealand-based Internet businessman and convicted hacker Kim Dotcom, his family knew that something was off.

Over seven frenzied days, Dotcom had become a leading purveyor of the theory that Rich, a staffer at the Democratic National Committee who was shot dead near his home in Northeast Washington last summer, had supplied DNC documents to WikiLeaks and was killed as a result. Multiple security analysts and an FBI investigation have tied the release to hackers with ties to Russia. D.C. police have said repeatedly that they think Rich was slain in a random robbery attempt.

According to experts and Rich’s family, the emailed invitation from welcome@mega.nz appeared to be an attempt to gain access to Rich’s email. Joel Rich, who monitors his late son’s Gmail account when new emails come in, did not click the link. Dotcom had not worked at Mega itself for years, but he was promising on Twitter to prove that the younger Rich had been in contact with WikiLeaks — and Fox News host Sean Hannity was telling his 2.37 million Twitter followers to be ready for a ­revelation.

Hannity had invited Dotcom to appear on his show for what he said on Twitter would be a “#GameChanger” interview. The implication: that Dotcom would finally offer evidence of his claim that Rich had sent internal DNC documents to WikiLeaks before his death.

All that began to unravel Tuesday afternoon when Fox News retracted a story that had claimed the same Rich-WikiLeaks connection, telling readers that the article was “not initially subjected to the high degree of editorial scrutiny we require for all our reporting.” Fox News did not respond to a request for comment, but Dotcom wrote on his website that he would not speak further about his allegations.

The latest revelation — that someone may have been trying to hack into Rich’s email — offered fresh evidence that the conspiracy theory is false. The family worried that Dotcom, or someone eager to prove him right, may have been willing to create a fake archive of emails from Rich, or crack a password to see whether Rich had passed on documents with a Mega account.

“It looks like someone set up a fake Gmail account, then used that Gmail account to create the Mega account,” said James Lewis, a cybersecurity expert and a senior vice president at the Center for Strategic and International Studies. “This part is pretty standard. Mega then checks with Gmail to see if the account exists, which is Mega’s somewhat cheesy way of authenticating identity. You then get to set up the Mega account. It’s a system designed to enable pseudonyms and fake identities.”

Mega.nz, a data security company that Dotcom founded, did not respond to a request for comment.

The episode also demonstrated how fake news can be flung from fringe media to the mainstream. A conspiracy theory that began on pro-President Trump message boards — a theory that Rich was actually a mole who wanted to expose corruption at the DNC — was fed by Russian news outlets including RT and Sputnik. The Daily Mail, Fox News’s website and several other mainstream outlets with large audiences churned through false information and leading questions, sowing confusion that Rich’s family struggled to combat. In addition to Hannity, former House speaker Newt Gingrich on Sunday said on “Fox and Friends” that the story was worth investigating, a sentiment he repeated in a short interview with The Washington Post on Tuesday.

“I don’t know anything about it,” Gingrich said. “I know exactly what has been said on the various blog sites . . . I think it is worth looking at.”

In a statement, Rich’s family told The Post that they were investigating whether someone attempted to gain access to Rich’s email account. “We are outraged that certain individuals continue to try to use Seth’s name and memory to advance their political and ideological agendas,” they said. “We hope people will think twice the next time someone makes an outlandish claim to have discovered new evidence in this case.”

A family spokesman went further, criticizing Fox News for fanning the flames.

“We are hopeful that in the future that Fox News will work with the family to ensure the highest degree of professionalism and scrutiny is followed so that only accurate facts are reported surrounding this case,” said Brad Bauman, a progressive communications strategist working with the Rich family.

Dotcom did not respond to an emailed question about the Mega account, but his story about Rich has altered since some attention-grabbing tweets. On May 16, he mentioned Rich for the first time after a follower asked what he thought of the conspiracy theory that Rich was tied to the release of thousands of internal DNC documents.

On May 19, Dotcom asked for Google to release the contents of Rich’s Gmail account, as well as two accounts that online sleuths had claimed belonged to him. Later that day, Dotcom said that he was willing to “give written testimony with evidence” that Rich had passed the DNC documents to WikiLeaks.

That attracted the interest of Hannity, who had devoted several segments of his radio and TV show to the conspiracy theory. Dotcom then claimed that he would be able to reveal what he knew after talking to lawyers.

But in a Tuesday message that Dotcom posted on his website, he claimed to know only that “Seth Rich was involved” in the DNC hack and that he would give his full statement after a “guarantee from Special Counsel [Robert S.] Mueller, on behalf of the United States, of safe passage from New Zealand to the United States and back.”

“I know this because in late 2014 a person contacted me about helping me to start a branch of the Internet Party in the United States,” Dotcom said. “He called himself Panda. I now know that Panda was Seth Rich. Panda advised me that he was working on voter analytics tools and other technologies that the Internet Party may find helpful.”

Dotcom provided no evidence to corroborate this. “We are unaware of any contact between Seth and Kim Dotcom and are not aware of Seth ever discussing the need for an ‘Internet Party,’ ” Rich’s family said in a statement.

Dotcom had made similarly grandiose claims before. In 2014, Dotcom claimed to have email evidence that motion-picture industry executives conspired with New Zealand’s government to send him to the United States, where he could be charged with several crimes. He organized a high-profile event, “the Moment of Truth,” days ahead of the New Zealand election. His guests talked about government spying; Dotcom drew attention to the email, which the studio decried as fake.

There would be another shot at the spotlight when Hannity and other conservative media figures asked whether Rich could be linked to WikiLeaks, thereby proving that there had been no Russia-linked hacking of the DNC. On Hannity’s show, a private investigator named Rod Wheeler, who had been paid by a conservative donor to investigate the murder, retracted his claim that Rich’s laptop was in FBI custody and contained evidence of a WikiLeaks connection. Neither allegation was true, according to Rich’s family.

“We know that Seth’s personal email and his personal computer were both inspected by detectives early in the investigation and that the inspection revealed no evidence of any communications with anyone at WikiLeaks or anyone associated with WikiLeaks,” Rich’s parents wrote in a column published Tuesday evening by The Post.

Yet for days, Fox News declined to correct or remove a story claiming that Rich’s “emails are in possession of the FBI, while the stalled case is in the hands of the Washington Police Department.” The story, published May 16 by Fox reporter Malia Zimmerman, contained specific details of what had been done and what had been covered up, citing a “federal investigator” in reporting that Rich “made contact with WikiLeaks.”

WikiLeaks’s Julian Assange had persistently fed rumors of a connection with Rich without providing evidence. He has offered a $20,000 reward for information about Rich’s killer, and he has used an interview with Dutch television, an interview with Hannity and several tweets to suggest that Rich’s case showed why WikiLeaks sources tread carefully. He has never explicitly said whether Rich was a source.

Zimmerman did not answer emails or a phone call about her story, which Fox retracted in its entirety Tuesday.

It was not the only flimsy lead. Roger Stone, a Trump ally who according to NBC News is cooperating with an investigation into whether the 2016 Trump campaign coordinated with Russian contacts, said this week that Rich had clearly given the DNC documents to a third-party source “in a floppy disk form.” But the source in his theory, a British ex-diplomat, had told Sputnik that he had heard about the hack secondhand — then told the Daily Mail that he had gotten documents in September, months after Rich’s death.

According to Clint Watts, a senior fellow at the Center For Cyber and Homeland Security at George Washington University, none of the “inside man” scenarios make sense. The FBI, he noted, had come to the DNC to report a data breach months before anything was published by WikiLeaks.

The collapse of the story came only after several conservative voices drew attention to it. On Monday, Rush Limbaugh told listeners that Dotcom was “renowned” and “world famous,” with a story to tell.

“This story is now starting to get legs, that Seth Rich was murdered, it was a contract hire killing because he was leaking to WikiLeaks,” Limbaugh said.

On Tuesday, Hannity told his radio listeners that he would keep fighting to disprove “this Russia collusion narrative” and be proven right.

“I will do the mainstream media’s job like I have for most of my career,” Hannity said. “All you in the liberal media, I am not Fox.com or FoxNews.com. I retracted nothing.”

Then, on the Tuesday night episode of Hannity’s show — the one that conspiracy theorists hoped would showcase the “game-changer” interview with Dotcom — Hannity said he had exchanged letters which Rich’s family and would not discuss the story.

“Out of respect for the family, I am not discussing this matter at this time,” Hannity said. “But to the extent of my ability I am not going to stop trying to find the truth.”

Karen Tumulty contributed to this report.