There are several reasons why you might receive a 403 error from the GSoC website. Here are some of the most common:
You are logged into multiple Google accounts in the same browser profile. We do not support multi-login, and suggest that you isolate each account to its own browser profile. (The site runs on App Engine, which does not expose the API to support multi-login.)
You do not have an account for this year's instance of GSoC. Even if you have participated in previous years, you must re-register each year. Students must register during the student application period. Mentors must request an invitation from the organization they wish to mentor with.