I started a business with a ton of student loans (almost 6 figures). I actually took out an extra student loan I didn't need and put it into Apple stock, using the gains to last another two months. And then I went into credit card debt.
I don't recommend doing all that. You can put away $20k pretty easily working in the Valley. That would be much less stressful.
Speaking as someone with over six figures of student debt (doh) and trying to do a startup at the same time, I'll say this much: I will, so long as I am as far in debt as I am, never go without a good paying day job. This means I am restricted to working on my startup for about 20 hours a week, and only after putting in a 40 hour work week. I can probably only pull this off because I have no kids and a fairly independent wife who will tolerate it if I spend every sunday working all day. Progress is slow, but I don't really have another option with student loan minimums over 1k a month.
Anecdotal, but, did (m)any people here on HN graduate and then start a business while still in debt with student loans?