Much has been written about Dolores O'Riordan since her sudden death this week, at the age of 46, in a hotel room in London. For a lot of people the outpouring of appreciation for her is a case of Big Yellow Taxi: "Don't it always seem to go that you don't know what you've got till it's gone ."

The Cranberries and O'Riordan occupied a particular position in Ireland. She was a megastar in the US, but O'Riordan and her band were never fully embraced on this side of the Atlantic. What's also notable is the number of people who didn't actually know O'Riordan. The Cranberries were never embedded in the Irish music industry, and didn't have the same tight relationships with the promoters, journalists, managers and PRs who tend to orbit successful Irish acts.

As Olan McGowan, an A&R scout at Sony in the early 1990s who is now an RTÉ producer, puts it, "The difference with The Cranberries in Ireland is that they never became a cultural phenomenon in the way other acts did, whereas in the States, just from the pure scale of the record sales, they were that. They were a defining band for American teenagers."

Like many of those affected by O'Riordan's death, Aileen Galvin wasn't a friend. She was just someone who was the same age, went to the same school and hung around the same city. "She was Limerick's superstar," she says. "Seeing someone from home make it big in Dublin was huge. Seeing someone who was ours on American TV, and hearing their voice on the soundtrack of movies and selling millions of records, it was hard to get your head around. Exciting and unreal. A life so far removed from everyone else's.

"All I shared [with her] were a few sneaky fags down the gardens when you were meant to be studying in the library. She'd a great smile, a gravelly Co Limerick accent, shy but wild, and you could see the cringe come over her as she stood to do a solo at the school Masses. But then she'd close her eyes and that voice would explode, especially as Gaeilge . . . It would haunt you, and for a few minutes you'd not hear a pin drop. With a rabble of young girls packed into the old convent chapel in Laurel Hill, commanding silence was some feat.

“She never courted the limelight,” says Galvin. “The rest of us scrambling for roles in the school musical and not a note in our heads. I guess that’s why the international-superstar Dolores and the schoolgirl Dolores always seemed two opposing characters juxtaposed.”

The record-company scramble at the beginning of The Cranberries' career was intense. In the early 1990s Michael Murphy was living in New York, working for a label called Imago, whose head of A&R, Kate Hyman, came across The Cranberries – then called The Cranberry Saw Us. As Murphy was Irish, she asked him if he knew the band. "They were still incredibly underground," says Murphy, who flew from New York to see them play at the Stables Club, in Limerick.

The wheels started turning, with several other labels beginning to sniff around. Over at Sony, Olan McGowan was also trying to get them signed. "I think Dolores was about 19 at that stage. I had the impression she was younger. She was painfully shy. Really, incredibly shy," he says. "There was a naivety. They needed an awful lot of refinement." But when he took their demo to Sony's offices in London "there was an indifference, a shrugging of shoulders. And I was playing Linger," which became one of the band's biggest songs. "I thought they were going to say, 'That's a hit.' "

Murphy and Hyman meanwhile brought The Cranberries to London, to play their first show outside Ireland, for their boss at Imago, Terry Ellis, to see. "Terry thought they were not stimulating, not interesting, not marketable, and had nothing to offer the mainstream marketplace," Murphy says. "I'm no expert, but I just genuinely loved the band."

Hyman's roommate in New York was Denny Cordell, who signed them to Island Records. When he died, in 1995, the band responded with the song Cordell in tribute.

Murphy remembers them at that stage as “incredibly nice people; ordinary, appreciative people. We were laughing and joking about Zig and Zag. They were not pretentious, very unfiltered.”

He criticises what he calls the “faux buzz” when the record labels were starting to circle. “It was so embarrassing,” says Murphy. “Here were these four really nice people. The adults, the people who run the music industry, are immature, manipulative, desperate. It must have been a horrific introduction to the music industry for them.”

The British music press portrayed the band through a lens of cynicism and sarkiness but later hinted at contrition. Murphy reads from a 1991 interview with the UK music weekly Melody Maker: "'To one side sit gallons and gallons of Lourdes holy water, to the other the pantry door is covered in flies, seemingly immobile, caught up in the slower pace of life that rules here.'

“You’d think he’d gone back to the 1400s,” Murphy says. “Dolores was incredibly nice, incredibly polite, incredibly open, honest, uncensored. The guys were a gang; they shared that banter that lads do. She seemed a little bit outside that circle, even at that early moment, and seemed to have different music tastes.”

He also quotes a Q magazine cover story on the band from 1996. "John Aizlewood" – the article's author – "described the early British press treatment of the band as bigoted: 'The weekly music press ambled Limerick-ward to paint a racist picture of stupid bogtrotters bemused at encountering street lighting and running water.' "

The G force of The Cranberries' ascent to fame was almost overwhelming. They split with their manager Pearse Gilmore. Geoff Travis, the founder of Rough Trade Records, stepped in. Their almost mythical support slot with Suede in the US saw them become bigger there than the headliner. TV pushed their videos in a way that had to make them superstars in the 1990s. With O'Riordan's magnetism, the band's huge songs, and enthusiastic American music television and radio, they were on their way.

August 1993 was a crucial time for O'Riordan and her band. It was the second week they had cracked the US charts – but the rock bands of the moment were polar opposites of The Cranberries: that year's Lollapalooza, one of the biggest festivals in the States, featured Primus, Alice in Chains, Fishbone, Dinosaur Jr and Rage Against the Machine.

“The landscape of the music industry was incredibly masculine at that moment,” says Murphy. “In comes this band from Limerick who haven’t had a great relationship with the Irish music press, they don’t have any champions, any mentors. Some of the British press think they’re fairies who have emerged from the magic spring . . .

"I just think, God, they were just victims of the moment of their triumph. There were no allies. They weren't part of a movement . . . The Cranberries were not celebrated in Ireland. I think that's our fault, more than The Cranberries' . . . I think Stuart Clark at Hot Press was one of the only constant champions that band had."

O'Riordan's voice was half gossamer, half razor blade. From the outside it appeared that her shyness on stage – she initially stood side on or even with her back to an audience – had been replaced by a fierceness. They released five albums in eight years, selling more than 40 million records. O'Riordan released two solo albums in a three-year period in the late 2000s before the band reconnected with Stephen Street, the producer with whom they were most associated, releasing the album Roses in 2012, and last year, Something Else, acoustic and orchestral versions of their most famous songs.

As the tide went out on the intense fame they has experienced in the 1990s, O’Riordan occasionally spoke about her personal issues, including her anorexia. In 2013 she talked about being sexually abused between the ages of eight and 12, about the impact of her father’s death, in 2011, of her periods of mania and her diagnosis of bipolar disorder.

Her mental-health issues became even more public in 2014, when she was arrested after an air-rage incident on an Aer Lingus flight from New York.

The Cranberries and O’Riordan’s stardom was made up of so many juxtapositions. “The music industry can be very brutal to women,” Murphy says, “and The Cranberries had no obvious contemporaries. They were never part of any movement. They never found their tribe.”

It does feel as though, as the years have passed, our appreciation for them has really developed. The songs – unweathered, still sounding as spine-tingling as ever – have gone the distance.

In 2012, promoting Roses by playing a live session for National Public Radio in the United States, O'Riordan asked the small audience for suggestions. "Any requests there, lads?" "Zombie!" someone called out. "Zombie? Yeah?" she responded, as if it would never have occurred to her to play that massive tune. "Zombie. Maybe, yeah. I need an extra guitar, though." She got the guitar, and launched into the tune with a "right, lads".