If you want D&D to reach a wide audience, and more importantly, the target audience that WotC seems to want (young-ish folks with disposeable income and time), you need to offer them something that they already want.
That's why we don't need a "basic" game. We don't need an "introductory" box set. We need a D&D Party Game. We need a game that people can play for an hour or two instead of games like Apples to Apples or Taboo. Adult party games do sell pretty well, and enjoy an audience which likes little games which they can gobble up while they're having cake and coffee at the end of a get-together. A game that Starbucks or similar cafes can stack in their stores for people to pick up while they're having a coffee. And it's easy enough for kids to play too.
First, cut out the DM. While I think the game is best served with one right now, it doesn't jive with the party game mentality of "open the box, read a single-sided page of rules, and get rolling". Replace the job with a deck of "dungeon cards" which let you randomly create a dungeon with hallways, different doors, and different challenges as you explore it. In terms of size, I think over-sized flash-cards would work the best to allow for good artwork and enough room for all the stats. Put a "blank" dungeon feature (room, hallway, etc.) on one side, and then when you flip it over, you could reveal a challenge (like a trap or a monster) or treasure. For the monsters or traps, put a short flavor-text blurb for what's coming at them. "A pack of slavering, porcine monsters with tusks narrow their beady, glowing red eyes at you. One of them lets loose a warcry and hefts its axe, and the others join the charge." Include a piece of Monster Manual-esque art and bare-bones stats for people to kill them and take their stuff. Resolve the fights by rolling a pool of d20s like Risk, and track "health" by taking away d20s as people get injured (and let people heal by recovering d20s).
Other rooms should include traps which are resolved like single-round battles. Players roll everything. Some rooms should include positive things too (think about the variety of things on the map of games like Heroes of Might and Magic). Springs of magic water that heal you, a wise sage who lets you see into the rooms around you, etc. Make sure all the rules fit easily on the back of a dungeon card.
Stick a few plastic miniatures in the box, and make sure all of their stats are simple enough to fit on a single card and that you can figure it out pretty easily. Put an evocative picture of iconic PCs on one side of the card, and stats on the other, so players can decide at a glance which character they want. Make them all cool, and sum up their abilities in a way that quickly and easily lets players know what they're in for. Keep the players on their toes by including a dragon miniature as a wandering monster who is trying to hunt the heroes down, and who promises to make quick work of them! The dragon snakes around the dungeon, sniffing out the heroes, always drawing closer, and the heroes need to figure out how to evade the dragon as best they can by finding a way through passages that the dragon can't fit through.
In the rest of the box, put in all the dice players will need. Ideally, simplify things so they only need d20s. Put in a one-page rule-sheet about selecting characters, exploring the dungeon, and how to win (include one or two scenarios, like finding a specific piece of treasure, slaying the dragon, or escaping from the dungeon). Emphasize that the players are a team, but to appeal to the party-game mentality of someone winning and someone losing, include simple rules that say "If you wish, two different teams may explore the same dungeon at the same time, but only one can win!"
Also include in that box an advertisement which tells players that there are other Adventure Packs available, which include Whiteplume Mountain, Sinister Secret of the Salt Marsh, so on and so forth. And on the reverse side, include an advertisement for the core rulebooks, telling people that the next step is to be the ones to create their own adventure. They get to create the heroes! The Dungeon Master leads them through an adventure which he designed himself! They can create any adventure they want with the core rules, and the only limit is their imagination! Include a link to the Wizards of the Coast D&D site and maybe partner with Borders to include a coupon for 10% off your very own Player's Handbook.
Draw them in with a party game that they can play for two hours over coffee and cake at the end of a party, one which stores can stock right next to the other party games in the board games section. One that has the D&D name. One that you can advertise as a party-game played by fun, smart, attractive adults all sitting around a table, laughing, and cheering. One that provides a gateway to the hobby of roleplaying, and breaks the notion that D&D is for fat, sweaty nerds who dress up like wizards and elves.
