Implementing the Bureaucratic Black Arts?
Success in a big organization has a lot to do with making friends with not just high level people (obvious), but also with people that manage paperwork for a living. Most of them are used to having people scream at them and give them a hard time. They build up a programmer-like cynicism since so many dismiss their contributions. *BE NICE TO THEM*
Taking care of them, writing them nice emails, taking 5 minutes out of your day to say "how are you doing?" is worth more than you can ever imagine. When I need anything out of the system, I now have "go to" folks that will help me navigate the system, exploit details that are not commonly known, and even bend the rules a bit.
When I cash in a favor I make sure and replenish the deed by dropping off donuts for the team, contributing to birthday gift funds, etc. Believe it or not, most of these folks are actually nice people that are trying to navigate the same mess you are. Be nice to them and you'll get far "in the system".
With respect to what another poster said about protect yourself -- that's true no matter how big or little the company. Make sure you take care of yourself. A good relationship with all the staff is a good way to accomplish that.