When you say start-up I assume you aren't talking about Facebook, Zynga, etc. You're talking about the companies with 10 people packed in basement?
If so, the answer is network, network, network. Talk to Duke alums in the industry. Most of the small start-ups don't post jobs, they have a need and they use their network to find someone to fill the position.
Another option is to look at the portfolio companies for the tech-focused VCs (they will be listed on their websites). If something interests you, contact the VC guy and tell him that you're interested in interning for one of his portfolio companies (he'll be relieved you aren't asking for a VC job).
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