I hate to sound like a total dork, but honestly? I probably couldn't. I've gotten so used to doing everything online that I'm not sure I could adjust to a non-Internet life.
How do I check my bank information? Online.
How do I keep in touch with my friends? Online. If I didn't have Facebook, I'd probably write a lot more letters...but I highly doubt most of my friends would respond, since they aren't in the habit and they would still have Internet.
How do I launch new research projects? Online. Before I start a paper, I always use Wikipedia to get a general idea of the topic. Don't get me wrong, it isn't my primary source of information, but it's a launching point. It's also the reference I always go to when I have quick question, like "Who is Josh Brogan??"
How do I record my daily thoughts? Livejournal. Online.
$10 million is a princely sum, to be sure, but I just don't think I'd be able to make the leap to a non-Internet life. Knowing this makes me feel rather pathetic...