Chris.
To start off you need to realise what "kind" of composer you want to be.
If you want to make it into the concert hall, knowing the president of Procter & Gamble won't help. If you want to make it into pop, knowing Penderevski won't really help. etc, etc...
Once you know what you're aiming really, repost and some more advice, I'm sure will come to your way.
You can either be the broad "classical" composer, or the "media" composer. Classical can be devided into different styles, as well as operatic, theatrical, installation composer, etc, while the media involves computer games, films, animations, ads, TV, etc.
all the above are differentl they need different people to netword, different knowledge even in music (who cares about computers and cubase in concert hall music? Who cares about quarter tones in ads music? etc), different degrees maybe (is a PhD in classical composition useful when you try to enter the media arena? Is a degree in production useful if you want to do... solo piano music?), and different experience. One who has many computer games under his belt, will he be able to score a good gig in films (the answer is no*). One who's written tons of ad music, will he be able to persuade LSO to play his music (the answer is no*).
and so on...
So once you get your ideas fixed you will need to following to become successful:
1. tons of luck (some people call it talent. Some people call it opportunities. Some people call it circumstance)
2. good looks (yeah, laugh!

lol)
3. The ability to write music. (yes, it is needed).
Now the above will get you your first step. You may even become successful (which reminds. You also need to define your definition of successful, btw).
After that the point is that you will need to sustain your popularity and be able to keep on being successful. In other words, many may get a first shot, few will get a second, very few a career. Just because one got a few computer games to score, it doesn't mean they will have a career ahead of them!
So in combination to the above you need to also have:
i. a personality. Who likes working with a dumbass? Who likes working with someone who is always late? Who likes working with a smartass?
ii. KNOWLDEGE (capital letters). You may get away in the shadows once or twice, but the big chances are that everyone famous KNOW what they're doing, with the exception of 1-2 people who excell in everything else however!
etc...
Somehow this post got bigger than intended... heh...
EDIT: HAHAHAHAHA! What QCC says, as always!
