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Cain says no way he harassed No. 4

FAMILY SUPPORT: Presidential candidate Herman Cain says wifeGloria is backing him amid allegations of sexual harassment. (AP)

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He did not have sexual contact with that woman — much less remember her name or even her face.

In a remarkable press conference yesterday, Republican presidential contender Herman Cain denied that he even knew Sharon Bialek, a former underling he allegedly groped after she came to him for job advice — and flatly dismissed every other accusation of sexual harassment lobbed against him, too.

“I have never acted inappropriately with anyone, period,’’ Cain said. “The charges and accusations I absolutely reject. They simply didn’t happen. They simply did not happen.’’

CAIN ACCUSER ‘WENT UP & HUGGED HIM’

The development came as:

* One of his previously unnamed accusers was revealed as a highly respected government spokeswoman. Karen Kraushaar, 55, called for her, Bialek and any other alleged Cain victims to hold a press conference to “present together what happened, and the court of public opinion can consider the allegations as a body of evidence.’’

* Bialek insisted that her 13-year-old son pushed her to come out with her accusations, saying he told her, “Mom, you have to do the right thing. I think you need to tell on him.’’

* Cain’s camp delivered a blistering attack on Bialek, running down her shady financial past and a custody battle — and even disseminating to the media the actual case-file numbers from financial judgments against her, including two personal bankruptcies.

* The Rev. Al Sharpton blasted Cain for accusing “racist” liberals of being out to get him, adding, “I think now his own inconsistencies is what has made this a story.”

But the married former pizza mogul was defiant — even though he acknowledged that “there will probably be others’’ coming forward to accuse him, fueled by his political enemies.

He said that as he watched Bialek level her charges against him on national TV on Monday, “My first response . . . was, ‘I don’t even know who this woman is.’

“I watched her again today . . . sitting there [during an interview]. I didn’t recognize the face, didn’t recognize the name or the voice.’’

Cain acknowledged that there’s a “remote’’ possibility that his memory could just be failing him, but he doubted it.

He said he would even take a lie-detector test to prove his innocence — although he quickly added, “I’m not going to do that unless I have good reason to do that.’’

When a reporter asked whether he was downplaying the seriousness of the charges leveled against him, Cain answered:,“Sexual harassment is a very serious charge. Yes, I have seen instances . . . and if I saw it . . . I dealt with it immediately.”

But “it’s not just men who harass women,’’ Cain said. “I also have seen situations where women sexually harass men.’’

The darling of the country’s conservatives blamed “the Democratic machine’’ and anti-business people for trying to bring him down.

As to whether he might quit the race, Cain said, “Ain’t gonna happen.”

Bialek’s lawyer, Gloria Allred, demanded that the Senate subpoena Cain and all of his accusers.

“Let’ s have everybody testify under oath,’’ she told CNN.

Kraushaar appeared to support the idea of confronting Cain publicly.

Her lawyer said that when she worked as a rep for the National Restaurant Association while Cain was its president in the late 1990s, she complained of “multiple incidents over multiple days . . . that constituted sexual harassment” by him.

Married for nearly 25 years, the attractive blonde had stayed in the shadows to abide by the terms of her settlement with the NRA over the alleged harassment.

Kraushaar, now the communications director for the Inspector General’s Office of the US Treasury Department, is believed to have gotten $45,000 in the settlement.

But since being outed by the iPad newspaper The Daily, her story “is now no longer a private matter but a matter of public interest,’’ Kraushaar, a registered Republican, told USA Today in suggesting a joint presser for her and the other women.

Of her leaving the NRA in 1999, Kraushaar told the New York Times, “When you are being sexually harassed in the work place, you are extremely vulnerable. You do whatever you can to quickly get yourself into a job, someplace safe, and that is what I thought I had achieved when I left.”

One of Kraushaar’s neighbors in Germantown, Md., David Jervis, told The Post, “I don’t know anything about the incident, but she’s not a kook . . . If she says it’s true, it’s true.’’

Cain tried to brush off Kraushaar’s accusations, saying he’d see her at work only “periodically’’ — and that the one complaint she made against him was “found to be baseless.

“There was no legal settlement. … She could not find anyone to corroborate her story,’’ Cain said.

Of the complaint, he said, “One day in my office at the NRA, I was standing next to Ms. Kraushaar, and I gestured . . . [and said], ‘You’re the same height as my wife,’ because my wife came up to my chin.’ ”

Cain’s camp took harder aim at Bialek.

Under a release titled “Who is Sharon Bialek?’’ the campaign sniped that she’d had nine jobs in 17 years.

It also talked of the bitter custody battle over her love child with a well-off Chicago marketing executive.

The baby daddy, West Naze, charged in one filing in 2000 that “Sharon’s significant mental and emotional problems impede her from properly caring for [their son].’’

Eventually, she got custody and West was ordered to pay her child support, which amounted to nearly $67,000 last year, NBC reported.

Hitting the TV morning-show circuit yesterday, Bialek insisted to ABC, “I was not paid to come forward [against Cain].”

Fox News asked her about the fact that she lived in the same building as Cain political foe David Axelrod, a top aide to President Obama, and she said she had no interaction with him.

Seemingly adding to Cain’s woes was yet another woman who surfaced less than 24 hours earlier to say that while working for the USA International Development group, she felt harassed by Cain.

Donna Donella, 40, of Arlington , Va., told DC’s National Examiner that her group had paid for Cain to fly to Egypt in 2002 for a talk.

One woman in the crowd who asked him a question was an attractive 30-year-old Egyptian.

“And after the seminar was over, Cain came over to me and a colleague and said, ‘Could you put me in touch with that lovely young lady who asked the question, so I can give her a more thorough answer over dinner?’ ” Donella said. Shea refused.

Cain then replied, “Then you and I can have dinner,” Donella said. She did — with two other co-workers.

Additional reporting by David Seifman