Remember a band called Radish? Probably not. We were all in early high school when they were christened the Next Big Thing — and so were they, actually. The Dallas grunge band, led by 16-year old Ben Kweller, represented just about every high school kid’s dream come true. While we were all daydreaming about Rolling Stone, Radish was featured in its pages. While our moms were driving us to rock shows, Kweller was jamming with rock stars. They were compared to Nirvana. They were compared to Everclear. They were compared to Silverchair (how could you resist?). In retrospect, the hype may have been just that: hype. But then again, it was 1996. Kids still skateboarded. Courtney Love was still cool. Seattle was still Planet Hollywood-free.

So what happened?

Well, nothing, really. After an embarrassingly intense bidding war, Radish signed with Mercury Records. And then . . . that was it. As is usually true of the Next Big Thing, Radish drowned in its own hype. Its reviews were lukewarm, its music was passé and its members — including Kweller — were forgotten. Grunge rock was dying and the infant Radish would be one of the first casualties.

Fast-forward five years. Kweller is 20 now, has just released his debut solo album, “Sha Sha,” on Dave Matthews’ ATO Records and is touring with the much-hyped Dashboard Confessional and Anniversary. Half a decade later, he’s in Rolling Stone again — this time with a three-star review that calls his melodies “impressive” and his slight Texan drawl “fetching.” The Mar. 14 Dashboard concert he opened at the Great American Music Hall sold out weeks in advance.

A lot has happened between now and 1996, according to Kweller. After Radish disappeared, he grew up, packed up, moved to New York City and started over the old-fashioned way: booking his own shows from the driver’s seat of a gray Volvo, with an acoustic guitar in his trunk.

“The difference between this and Radish is that I’m really doing everything I want to do, and I’m running the show, and it’s all coming from some real place instead of from some A&R guy’s desk.” Is it different being on the tiny ATO label? “So different,” said Kweller. “They give everybody complete creative control.”

Ben Kweller looks his age. He is a precocious, stripy-shirted, Chris Van Dyke-like boy, and onstage, he leaps around like a child with ADD. The sound coming from the speakers, though, is undeniably grown-up.

Kweller says his influences range from the Beatles to the Violent Femmes, from Marvin Gaye to Weezer, from Neil Young to Nirvana.

“I like heavy stuff, I like soft stuff, I like ballads . . . I like everything!” Kweller laughed. “That probably comes across in the music.”

It does. “Family Tree” is so Beatles-influenced that it is almost a cliché, while the catchy “Wasted and Ready” could have been written by Weezer. The album’s best songs, though, are the ones that you can’t quite sort by influence. In the end, the most authentic songs on the album are the ones that sound least like other artists. Songs like “How It Should Be (Sha Sha),” “Falling,” “Walk on Me” and “In Other Words” are the ones that you might be pointed to if you were to ask, “What does Ben Kweller sound like?” These songs, all deceptively straightforward tracks, brim with the kind of wistful joy that only sounds honest coming from a 20-year old, but with a vocal control and instrumental complexity that is remarkably mature — from the cleverly placed triplets in “Falling” to the gorgeous melody in “Walk on Me” (that’s the one with the “fetching” vocals). It is clear from these songs — and from the way Kweller performs them live — that he has a talent that puts him several rungs above the rest of his peers.

Well, that and a refreshingly dedicated fascination with playing music — even after an early disappointment.

“From 15 to 20 years old you change so much. You’re still exploring and finding yourself. [Radish] was my high school punk band. Everyone has a garage band, but, like, mine got signed. That’s the difference. I mean, that’s really all it is, just growing up and finding new things that we all love.”

Once again, Kweller’s living a life that the rest of us only daydream about. He gets to have a beautiful girlfriend who comes on tour to sell his merchandise (see Lizzy). He gets to be indifferent about drugs (“I don’t know, I guess I feel like everything in moderation’s okay”). He gets to think of songs while “fucking around in a hotel room.” He gets to have the Moldy Peaches’ Kimya Dawson sing back-up on his album, and then he gets to say this about it: “It’s so cool to collaborate with friends. That whole New York scene, the Strokes, the Moldy Peaches . . . they’re all great people.” And he gets to make music. Really good music.

“I just tried to make shit happen the best I could, you know?” he says.

It’s happening, Ben. It’s happening.