As a Startup Weekend organizer, I can tell you that getting sponsorships is a whole lot of work. Startups don't have much cash so they prefer to donate in-kind services, i.e. give away free product, which isn't so bad when you run a competition (like what we do) but such contributions still don't pay the bills.
There's no silver bullet to get sponsorships. Even if you have an inside connection and not cold-calling there are other factors, such as their finances, plans, time of the year, and your event's mission, that are far more important. So do your homework, craft a compelling reason to sponsor your event, and then spray-n-pray. However, it doesn't mean you should spam every startup you know - you still need to have some fit but the list should be bigger than what you need.