I've periodically had the opportunity to speak with some influential and progressive people, the kind that might be interested in funding the next CoinLab venture. Almost all of them have been completely, and somewhat surprisingly, unfamiliar with Bitcoin. Those that are aware of it regard the system warily, as something too new to be taken seriously yet.
Concrete examples and tailored analogies tend to be most effective; weusecoins.com does a great job of that from a consumer viewpoint. For business/entrepreneurial and high net worth types, the interest piques when I mention the potential to move arbitrary amounts of funds across borders and nearly instantaneously, especially when speaking about selling gold for bitcoins in one location and reversing the exchange upon arrival at the destination.
Whenever fears about Bitcoin disappearing come up, I compare the system to bamboo or ivy. Anyone who's wanted to get rid of either knows it can be an exceedingly difficult task, even borderline impossible if there's enough growth. If they press for a deeper answer, I note that the technical structure is built on proven technologies decades old (hitting the mathematics point you made), and that nodes are geographically dispersed such that the US would have more than a hard time shutting off Brazilian or Chinese participants. I try to avoid BitTorrent network comparisons at first because of the unwarranted negative connotations.
On the question about what Bitcoin is backed by, I've found that it gets the target's brain working when replying with this question: Where does the value of the Internet come from? For the more business-oriented, that can be modified to: What is the value of your contact network? When asked to put a number on something so nebulous but integral and ubiquitous, only a handful so far have been able to say more than 'highly valuable' without quantifying - a few times it's been stated as the most important part of the owner's company.
That's usually where I've seen a trigger hit, telling me the person realizes Bitcoin is more than it seems at first glance, and the impact has led to inquiries (some up to months afterward) asking me how to get started. Most of the time, they also want to know if and how they can use it with people they know. For that, I start with the analogy that it's like sending a message to an email address, only the message contains the number of bitcoins to be sent.
I sometimes suggest they also buy mining bonds to profitably support the network, but BitInstant is one of my perennial recommendations
+1
You misspelled SolidCoins