Your ideas are not fighting.
Ideas don't matter. Say that over and over again until it sinks in. The fact is, all those other things -- connections, designers, fame, money - might be the key ingredient (or part of the recipe) to make an idea like that take off in a global marketplace. Or not.
We see this with these categories of ideas all the time. Things like cloud storage. Everybody did it -- with all kinds of famous people and different strategies, some expensive, some not. It was finally the Dropbox guys who got it working.
It's like baking a cake that nobody has ever made before and without a recipe. Some cake ideas need fancy ingredients to make work. You're not going to have those. The real trick, however, is taking the ingredients you have and forming the best cake possible, the one the most people want, not looking at what the other guys are doing.
It not a true statement that only big budgets and famous people can create large startups. Perhaps it helps. In either case, don't know, don't care. Focus on what you have. Let those other folks do their own thing. It's better to spend your afternoon finding one person who likes what you are doing and is a customer than it is to spend your energy on this kind of stuff. If you have a customer acquisition model that you've worked out and is humming along, you are doing awesome. The mind plays all kinds of tricks to get us off-path in our startups. To keep us from focusing on what's really important.
Mind your knitting.
ADD: You can look at this the complete opposite way as well. I blogged about the drawbacks money can bring to the startup process just a few days ago: http://www.whattofix.com/blog/archives/2012/02/being-rich-wi... It's the creative assembly of the ingredients you have at your disposal that matters, that you should be concentrating on. Not thinking for a second about some resource you do not have available. It's just a waste of time.
I understand this advice sounds trite and programmed. Something along the lines of "you can do anything!"
I don't mean this as facile. The problem here is by focusing on the ingredients of a startup, and not the assembly, we're not left with anything to talk about. Do you need publicity do do a startup like X? Some people will show you examples of how the answer is "no". Some others will show how the answer is "yes". There's just nothing useful there -- it's the assembly. People can wave their hands around on either side of the discussion and make broad pronouncements, but nobody really knows. Could you start a business selling Porsches if you're poor? I'd guess probably not, but I don't really know for sure. Nobody knows until somebody does it. Startups are new business engines that didn't exist before. It's the quality of the assembled engine that matters, not the individual pieces. Extrapolation and generalization are not very good tools for talking about them. That's the way it works.
If your question was a very detailed one about the exact configuration of your marketing and customer funnel, and the exact strategies being used by your competition, along with data, we would still be guessing a lot, but at least we might get some traction on the problem. But once again, we'd look at perfecting the model using the resources you currently have. But if your question is just guys in coffee shops versus famous people, nothing much useful is going to happen.
So I'm not trying to make an overarching "buck up!" statement. I just don't think you can do any kind of analysis with the question as it has been posed.
I don't think that point can be emphasized enough: your idea is not a unique snowflake. It's the other factors that actually determine success. The idea is the absolute easiest part of anything worthwhile you'll ever build.
The mainstream media sells the notion of the magic idea, the overnight success, etc. I came of age in the initial era of the dotcom fantasy. It was very easy to be sold by the 24/7 press coverage in the mid to late '90s, that magic ideas were worth billions because of how fast bullshit companies were acquiring zillion dollar valuations. Of course you can count on one hand how many dotcom billionaires made it out alive from that era.
It took years, a few failures, and a lot of reading to correct the flawed assumptions I had taken on. I owe a lot to countless web authors, from the likes of Chris Dixon to Mark Cuban to things people like Andreessen and Horowitz have written, and so on and so forth. I think those guys most valuable contributions to other entrepreneurs is in what they write, not the money they invest - they'll have impacted radically more entrepreneurs with the writing.