It’s hard to remember now, but about a dozen years ago, Ellen DeGeneres was dead in the water.

The nice girl from New Orleans with the sunny disposition and the squeaky-clean comedy act had been a star with her own sitcom, “Ellen.” But then she had come out as gay, such big news at the time that it landed her on the cover of Time magazine. Then her character on the show came out. Then she and her partner at the time, actress Anne Heche, were very kissy-kissy in public.

The show tanked, the relationship tanked, the career tanked. DeGeneres found herself, at 40, angry, depressed and out of work.

“I lost it all,” she’s saying on the phone from her office in Los Angeles. “I was angry and hurt and felt sorry for myself.”

For the next three years, the only thing she had to work on was a voice-over in an animated movie. About a fish. It paid scale. Hahahaha! Fish! Scale!

Cheer up, people! It’s Ellen! Happy! Witty! Funny!

You thought DeGeneres, who’s coming to town Monday night to receive the Kennedy Center’s Mark Twain Prize for American Humor, was going to sit around and mope about the bad old days?

The film was “Finding Nemo” and all it did was gross some $920 million worldwide.

DeGeneres, who voiced Dory, the super-cheerful little blue tang with short-term memory loss, is now much, much bigger than she was before The Fall.

Her eponymous talk show has won dozens of Daytime Emmys and made her one of the wealthiest women on the planet. She earned roughly $53 million last year, Forbes magazine estimated in May, about the same as Rihanna and Lady Gaga. The magazine also rated her the 47th most powerful woman in the world. She’s hosted the Emmys and the Academy Awards. She has her own music label.

“It was a very hard time for me, a low point, but I also am more grateful for that than just about anything else,” she’s saying down the phone line. “It’s an invaluable experience to find out who you are. It’s a very cushy life we live here, surrounded by people who make you feel you’re great, and it’s a bubble. . . . I grew and became a much more compassionate person.”

Monday night, at the Kennedy Center show – it will be taped for broadcast on Oct. 30 on PBS stations – she’ll be feted by guests including Jimmy Kimmel, Steve Harvey, Kristin Chenoweth, Lily Tomlin and John Leguizamo.

She and Harvey have been friends since their days headlining gigs in comedy clubs. Now he hosts his own talk show, and it serves as the lead-in to hers in several markets.

“She’s got that ‘it’ factor,” Harvey says. “She’s got that thing that’s hard to put your finger on. . . . I had to move a lot of stuff around to do (the Twain ceremony), but for a person who has been as kind as she has to me, it was an honor.”

Cappy McGarr, a Kennedy Center board member who helped found the Twain Prize in 1998 and who is an executive producer of the show, says DeGeneres’s contributions are in line with those of previous recipients, who include Richard Pryor, Carl Reiner, Whoopi Goldberg and Billy Crystal.

“She’s just a great humorist and satirist, like Twain,” he says. “She’s blazed a path.”

With the show lights off and in retrospective mode, DeGeneres, now 54, comes across as good-natured but more serious than her onstage persona. She’s polite and ad-lib funny – in discussing “Nemo,” she speaks whale in the Dory voice! – but it’s still clear that she’s talking business.

The conversation, and the attendant logistics of arranging it, are a small window into the complexities of her particular stock in trade.

She’s made tens of millions of dollars by being not just funny, but by selling an image (by all accounts entirely genuine) of being nice, pleasant, witty, kind, generous, cheerful and family-friendly. She doesn’t do snark, she doesn’t do profanity.

Hilary Estey McLoughlin, president of Telepictures, the Warner Bros. company that produces and markets Ellen’s show, says it’s been on-air for a nearly a decade because “it has a universal joyfulness that isn’t common. We’ve built the show around that, her personality.”

In short, what viewers bond with is the idea that Ellen (of course you’re on a first-name basis) seems so approachable that you could just plop down next to her and chat . . . except for the fact that you cannot just plop down next to her and chat.

Example: Even with a month’s window, her staff said DeGeneres did not have 30 minutes for an in-person interview for this story. Half an hour by phone was allotted – and at the stroke, an assistant told her to cut it.

Mary Connelly, one of the show’s executive producers, says that proficiency is one of DeGeneres’s key off-screen talents. “She’s extremely efficient” in the workaday aspects of running a show with 75 or so staffers and three dozen crew members, Connelly says.

Staff starts arriving about 8:30 or 9 a.m., DeGeneres arrives at 10:30 for a first call at 11, Connelly says. “If she’s on a call when it’s time for a meeting, she ends the call right there.” The show and monologue are honed and refined right up until the 4 p.m. taping in front of a live audience.

Most of the time, taping takes “an hour or less. We’re more or less live to tape.”

You want to know how to make it big in this business? Be professional. Be pleasant. Be efficient.

Elliot and Betty DeGeneres were not show business people.

He was an insurance agent; she was a real estate agent and a substitute teacher. They had two kids, Vance and Ellen. They lived in Metairie, a suburb of the Big Easy, and later in New Orleans proper.

 Vance DeGeneres, who has had a terrific career in music and television on his own (he is now head of Carousel Pictures, Steve Carell’s production company), remembers his dad joked and his mom played piano and violin, but there certainly wasn’t an artistic environment to mature into.

Their parents divorced when Ellen was 13. She went with Mom. Vance, four years older, went with Dad. (Brother and sister are now close, and see each other a few times a month.)

Ellen DeGeneres remembers writing all the time – poetry, stories, songs – but didn’t start with comedy until she was in her late teens. She did a semester at the University of New Orleans but dropped out. She was a waitress at T.G.I. Friday’s. She shucked oysters.

She started doing comedy at any local club that would have her. When she saw a new place, Clyde’s Comedy Corner, post a sign that said they were looking for an emcee, she applied. “I think if someone else had stopped by before me, he would have hired them, too,” she said.

She hit the business full-time in 1982, took off on the road and wound up in L.A. Her first sitcom, “Ellen,” hit the air in 1994.

It was no secret to friends and family that she was gay – she told her mother when she was 20 – but when she came out publicly on television, it turned into a nightmare. Jerry Falwell dubbed her “Ellen DeGenerate,” and she became, for a time, a lightning rod of sexual politics.

“It was hard for me seeing my little sister treated like that,” Vance DeGeneres remembers. “You get that playground feeling, ‘Hey Falwell, meet me at the flagpole.’ “

But when the dust cleared, it turned out DeGeneres was fine. She did “Nemo,” she put together a tour of new stand-up material, and she had already begun a happy relationship with Australian actress Portia de Rossi. (They married under California law in 2008.)

Telepictures asked her to do a daytime talk show, even though some television station owners were leery that she might have some sort of “gay agenda.”

The show debuted on Sept. 8, 2003. It built slowly and just kept going, buoyed by a slew of awards, and is now tops for daytime talk shows.

“She finally found what she’s best at and what she should be doing,” says Vance DeGeneres. “As good as she was at the sitcom and as funny as it was – what she’s doing now, it’s just sort of effortless.”

In this context, with a career built, lost and regained, Ellen says she’s at peace, a grown-up having a good time.

“I appreciate the (Twain) award and I’m flattered of course . . . but (awards) don’t mean everything to me,” she says. “What means the most to me is that I’m living comfortably in my own skin. I’m happy. I’m happy every day, I’m happy if someone gives me an award or if someone doesn’t give me an award.”

Let’s wrap this up at the beginning. Let’s go to Nov. 28, 1986.

It is the night of her first appearance on the “Tonight Show,” which made her a star.

She’s sitting backstage in the greenroom. Vance is next to her. “I think I was more nervous than she was,” he says.

Now Carson is introducing her. The stage curtains part, music blares. Here she comes, black pants, loose gray blouse buttoned to the neck, her hair in something approaching a mullet. (It was hip back then, kids.)

 “Thank you,” she says. “Hi.”

She can’t see the audience at all.

“It was so dark,” she remembers now. “I really couldn’t see anyone.”

She goes into her first bit about how she’s 27 but looks 23. Runs in the family, she says. Her grandmother is 97, but looks 93.

What she was thinking: “There’s Doc Severinsen and Ed McMahon . . . they looked like giant puppets from a Macy’s Day Parade.”

A bit about how terrible her family was. If the house caught on fire, her dad was to grab the pets, her mother the jewelry, her brother to run for help. Tiny pause, her trademark even then, and. . .”They told me to try to save the washer and dryer.”

The audience bites. Bright smile, quick, while they’re laughing: “I used to wander around the woods when I was a kid” – pause, let it hang, eyes drop – ” ’cause my parents would put me there.”

Big laughs. And then, somehow, she’s almost four minutes in. For the close, she leans on the first comedy gag she ever wrote, a phone call to God.

It began in tragedy, when her girlfriend at the time was killed in car wreck, and DeGeneres, then 20, wanted to ask God how such a beautiful life could end so young, in such meaningless fashion. But instead, it came out as her asking God about the usefulness of fleas, which had infested her dump of an apartment.

So, nearly a decade later, she puts her right hand up to her ear, thumb and pinky extended, a make-believe phone. Flop and her career goes backward. A home run and you might someday be running your own talk show and making $50 mil a year.

“Yeah, hi God, this is Ellen . . . Listen, if you want to – sure, I’ll hold on.” Pause. To audience: “Somebody’s at the gate.”

There’s a beat. They get it, love it.

She gets a chance to ask about fleas, God says something about jobs in the flea collar industry, sneezes (“God bless you, or bless yourself”) . . . and then wants to tell a joke.

“You got a joke for me?” DeGeneres says brightly into the phone. “I’d love to hear it. Go ahead.”

Pause, listening.

“Who’s there?”

God is telling knock-knocks. She pauses, letting the audience get it. They love it.

“God who?”

Pause.

“Godzilla. Oh. Incredibly funny.” Nodding, rolling her eyes to the audience. This God guy isn’t so bright.

“And another one? Oh, sure,” sarcastic.

She wraps it a minute later. Music, applause, whistles, and . . . Johnny is calling her over to the desk. She is the first female comedian to receive the invitation.

“That’s very clever, very fresh,” Carson tells her. “It’s good material.”

She is a little awestruck. There’s a bit of banter and then Carson says, “Will you come back with us soon? You’ve got an open invitation.”

Ellen DeGeneres, a quarter century later, still in America’s living room.