Since you'll be in California, you can take advantage of California Labor Code Section 2870-2872 ( http://caselaw.lp.findlaw.com/cacodes/lab/2870-2872.html ), and do your startup (that doesn't relate to the internship-company's business, nor result from the work you do for the company) on your "own time
without using the employer's equipment, supplies, facilities, or trade secret information".
Then, you'll get your pay from the summer internship (if they're not paying you, GTFO; you'd essentially be paying SV rents for the "privilege" of working for them!), and have a head-start for the winter round. You'll also have gotten more done self-fundedly, which will help you stretch any stipend you might get from YC.
Since you'll be in California, you can take advantage of California Labor Code Section 2870-2872 ( http://caselaw.lp.findlaw.com/cacodes/lab/2870-2872.html ), and do your startup (that doesn't relate to the internship-company's business, nor result from the work you do for the company) on your "own time without using the employer's equipment, supplies, facilities, or trade secret information".
Then, you'll get your pay from the summer internship (if they're not paying you, GTFO; you'd essentially be paying SV rents for the "privilege" of working for them!), and have a head-start for the winter round. You'll also have gotten more done self-fundedly, which will help you stretch any stipend you might get from YC.