However, a lot of companies that post jobs at UW also post them online. RIM for example hires hundreds of students from UW every term and their entire application process is online so you're probably not at a disadvantage there. Microsoft has their recruiting sessions here every few days it seems, so just attend one of those and hand out your resume. Now that Google has a branch in town just attend one of their sessions too.
If you're specifically looking to work for a startup, your best bet is to look up companies in the Accelerator Center (north campus, in the Research and Technology park.) There are about 15 startups there now. Terrapath and SuitedMedia are on a hiring binge, so just walk in there and talk to the president, you'll probably have a job on the spot. Don't be afraid, the guys there are all only a few years older than you, so don't feel intimidated at the prospect of just coming in and talking to the boss :)
I've been wondering for a while how much of a disadvantage I am in terms of getting an internship like this because I am not in the co-op program (besides advice and employment courses), as an employer do you give this much thought? (sorry to go off topic; I have talked to students about this but I figured I should jump at the chance to ask an actual employer.)
By the way, any chance you will be at BarCamp?