We're not a YC startup, but we found a designer who doesn't typically do web sites -- he specialized in storefronts, t-shirts, skateboards.. In other words, someone who didn't have any predefined notion of what to do on the web, someone whose core skill is to get a message across in milliseconds and to draw people in.
It worked out really, really well for us; it may be worth your while to look outside typical web designers. That said, we already knew what the application flow would be like, so it was a matter of 'skinning' for us -- color scheme, iconography, etc.
I congratulate you for finding a non-web designer who was able to get the job done well for you.
In my experience traditional print designers generally do not do a good job of creating a website design. They don't understand the deal with background images or what is and isn't possible, they prefer to use nonstandard fonts (easily fixed) and they typically don't understand what is and isn't possible with the technology being used.
Incidentally, we did get some proposals from other, more experienced web designers, but they all looked too formulaic and, er, web-site-ey.
dkokelley may have some good points, too.. It could've gone very wrong, especially if our site interaction was much more complicated (and surely someone else will think our design is a train wreck anyway ;) ), but I'm very glad that we took a chance on it.
In the end, the key was really that we were all just seeing the vision of what we wanted the same way.
It worked out really, really well for us; it may be worth your while to look outside typical web designers. That said, we already knew what the application flow would be like, so it was a matter of 'skinning' for us -- color scheme, iconography, etc.