Being the "right" gender (assume you mean female?) with a solid Computer Science degree wasn't enough to get my foot in the door to talk to anyone there either.

Being the "right" gender (assume you mean female?) with a solid Computer Science degree wasn't enough to get my foot in the door to talk to anyone there either. They're picky, elitist, and unless someone already there recommends you they won't even talk to you. At least that was the case before I got Amazon on my resume. Now it feels like every company on the planet wants to recruit me, including Google. I know a lot of people at Amazon who didn't have connections and didn't have a degree from an elite school (or a degree in CS at all in some cases) and they were still great. I'm sure google would never give them the time of day. The one person I do know who works at Google is awful to be around (he is the "wrong" gender and race btw and went to the same school as me, but got referred). Google is all he talks about. I invited him to a party once and he actually started working on his laptop mid-party and snapped at me when I came over and asked him what he was up to ("It's confidential!" he said as he closed the screen and left). So feeling rejected sucks, but maybe you dodged a bullet there.