Join a larger startup that needs people to do joe jobs - customer support, account manager, etc. Suck it up, work your ass off, learn all you can, and get yourself promoted to something interesting. (Larger startups are still fairly fluid - at least compared to the broader corporate world.) Product management worked for me, but your experience might vary.
Once you've got a couple years of experience, and you've done something a little more meaty than entry-level work, you'll have something more to offer an early-stage startup.
EDIT: I graduated as a Geography major, with the pitch being that cartography is a very skilled form of information architecture and interaction design, as we use maps both as art and as a useful, tailored tool; geographic information systems mean I have experience working with demographics, statistics and spatial analysis; multiple anthropology courses mean I can research and present analyses on both the developing internal business structure and on our customers; philosophy means I can think critically.
When I get a generic CV I'm getting told what qualifications the person has, but rarely am I told what they might do for me to justify their wage. What skills do you have? Why are they useful to my business? Why will employing you make my company more valuable?
If I take funding for my company, the level of funding indicates a valuation of the company. If I take on an employee I'm saying that the value of the company rises by about 5 times their salary.
It's the same with a startup. How do they know you can do things that they will need done? Answer that question, directly, without hesitation, and with convincing examples, and there's a good chance they'll take you.
