I'd like to work in a company to which I can contribute in a more meaningful way — not necessary a startup. A company with a real product and respect for engineers blended into their culture (or even better, engineering-driven) would be a dream place.

OP applied to Google and Facebook. He's not looking for work at a startup. He's desperate for a place of work, and that's it.

He isn't desperate for a place to work. He already has a job. Like everyone else, he wants to be feel like his work matters. After developing for a long time, I feel like thats what you crave the most. Working with other passionate people, hopefully most can be smarter than you and working on something that is meaningful that you can be passionate about.