Do you live in the Valley, or would you be moving here for the summer to do your internship?
Can you afford to not work and not take the internship this summer? If you can, why not pursue the idea anyway. If you get in to YC, great. If not, keep working on the startup and see where it takes you.
Why are you taking an internship? One of the main reasons to take an internship is to get job experience, and I'd say that starting your own business is pretty good resume-able experience. The vibe that I'm getting in the Valley right now, is that if you want a job, and you have decent skills, you shouldn't have too hard a problem getting it. It's an employee's job market right now. So, I wouldn't worry about screwing over your long term job prospects too much.
Another reason to take the internship is to get contacts. But, the kind of contacts that you'd make as an intern probably aren't going to be all that great. You're better off moving to Silicon Valley, starting your own business and doing the Meetup/conference things. Networking in Silicon Valley is pretty easy to do, and contacts come pretty easy. It's really a small town.
Another reason to take the internship is the pay. Which, is usually pretty low. If you're hard up for cash, I'd say that you're better off taking a coding job for the summer. From what you've said, though it doesn't sound like that's a big issue for you right now.
And, if you're worried about stepping on the companies toes--don't. Sending them a polite, professional letter explaining that you've decided to pursue other opportunities, should suffice. If they throw a fit or hold a grudge, you really didn't want to work for them anyway.