I have the complete boxed set of the old D&D cartoon, but I've never considered gaming it. I also use to own several of the D&D miniatures, some of whom appeared in the cartoon.
The cartoon is very poorly suited to D&D. It appears to have been loosely based on 1e AD&D, but none of the action in the stories is well suited to D&D and you'd be better off with a lighter more narrativist game engine if you want to capture the feel of the cartoons. (Now isn't that irony.)
For example, because it was a Saturday morning children's cartoon, things really are never injured or killed. They are merely stunned or knocked down. Virtually every attack the kids make is a narrated stunt of some sort with imagination highly privileged over logic or realism.
All that being said, when the cartoon came out I'd already owned the basic and expert boxed sets for a couple of years. It was I think a big influence on helping me recruit players for my first campaign, and with it's 'Star Wars cantina' feel and occasional orcs in the bar right alongside the humans, it did influence how I imagined the campaign world. And of the '80's nostalgia cartoons, it's one of the ones that has held up the best in terms of writing quality and production values.
Personally, I'd like to see the cartoon remade by the same team that did 'Avatar: The Last Airbender'. While I was disappointed by Korra (mostly because it lacked the epic scope of Aang's overarching 3 season story), I really think the basic story of orphans lost in a strange world is a strong one and deserves a full story arc. A modern cartoon with 'Previously on Dungeons and Dragons...' could overcome many of the limitations of the original cartoon. Some of the better episodes stand up so well you could polish them off and they'd play well today.
In general though, in any campaign, I'm uninterested in playing anyone else's story. If I were to run Chronicles of the Dragonlance, I'd run in with the player's invented characters, and not the stock characters of Weiss's and Hickman's imagination. Much as I admire what they did and still consider their striving for RPG as high art to be one of the highpoints of this new medium's short history, one of the best things about an RPG is you make the story your own.