A dating site, for example... At what point is it considered "up and running" and how does that happen? Or a service referral site like task rabbit?
Interesting question, but I don't really see it as a "chicken and egg" type challenge.
For a service startup business, you will still need an online presence. In the Lean Startup method we talk about MVP, the minimal viable product you can build to both test the waters and get paid. Why build a business that no one wants and therefore, no one will pay to use?
So, a better approach would be to test the waters first with a few phone calls. Is there a need? Want to be sure? Make one hundred calls. Then let's talk.
There are affordable ways to build a MVP.