Summary: No-one will buy an idea from you and do all the work. If you want to see your game realised, you must provide additional value beyond the original idea. This can take many forms. I suggest that the value you provide come from programming. But, as I mention in the alternatives, there are other ways in which you can provide value.
Knight666 hits it on the head. It doesn't matter how good your idea is, it's the execution that matters. So grab a big marker and write this somewhere you'll see it every day:
Ideas Are Worthless
You MUST read the question mentioned by Cyclops in the comments. Another way to think of the above statement is that since there is no demand for ideas, there is no market, they therefore have no value.
However I'm going to give you a different answer to Knight666:
Provide value with programming (Learn to code)
It is not as hard as you think. It is comparable in difficulty to getting your driver's license. Even if you know nothing right now, you'll be able to create a demoable prototype of your game within six month if you apply yourself dilligently.
If you're not willing to put six month of effort part time to see your idea realised, it isn't worth anyone's time.
Besides the fact that it's a useful all round skill to have, it will also allow you to interact with the people who make games. And this will be invaluable if you ever manage to get your idea off the ground. It's a no-lose scenario. You'll gain a valuable skill and insight even if you fail.
A major bonus is that while learning you'll build contacts with people who will be able to help you.
Then, instead of coming up to a company with some presentation, you can go:
Hey, I've built this in six month without knowing how to program. Do you think it's cool?
Even if they don't take on the idea, you're bargaining from a stronger position. Instead of needing the company for your idea to survive, you're looking for a partner to create something awesome with.
Have a look at This tutorial and see if you can understand what's going on. If you can, pick the one that looks clearest to you and start playing around. When you get stuck, ask here or on Stackoverflow for help.
Alternative ways of providing value
Another way to turn your idea into a reality is to get a programmer on board. To do this you'll have to build a personal relationship with that person, so that you're able to communicate your vision to them adequately. You will also have to Provide significant value. Contractors simply don't cut it for this kind of creative development unless you have enough cash to get great people.
I get ideas all the time. I could probably list off the top of my head 20 game ideas that haven't been made. The only reason for a programmer to work on your idea is that your involvement will significantly improve the chances of success.
If you're not going to program, then ask yourself this question:
What do I contribute to the success of the game besides the initial idea?
If your answer to that question is one of 'more ideas' or 'nothing' then give up.
If, on the other hand, you're able to things like:
- Drum up a storm on twitter
- Make crazy cool art
- Pitch to investors so well they beg to throw money at you
Then sell those abilities to a partner who can code.
Change the question from
What can I get someone to do for me?
What can I contribute to the success of this idea?
and you'll be in a much better position moving forward.