Startups have limited amount of funds to invest in their human resources so they will always be look for the best, the ones who take initiative, who goes all out to make something done right. I wouldn't give up hope just yet - start building something outside of what's formally required of you. Make an app, publish it, sell it and talk about it. You'll need to wear multiple hats in a startup so in addition to coding, if you can do the other stuff, you'll be a huge asset.