I was part of getting something similar off the ground the other year (Web Ecology Project, www.webecologyproject.org).

From what I've seen a Think Tank basically acts like an academic research group, but does commissioned research when possible. Getting started is a bit of chicken and egg thing, but once you're rolling you're kicking out research which seems to entice private companies into wanting to know more or use your tools.

With Web Ecology Project, we started off doing research on Twitter stuff, happened to grab every tweet out there on the Iran Election in 2009, self published a paper, and then boom. Tons of people wanted our data, expertise, analysis, etc. We weren't ready for this business-like shift, so we somewhat self-imploded for being able to run with it business-wise, but we're still doing research.