Tl;dr: We are more than just another Yahoo Answers or forum, but we are presenting ourselves in exactly the same way; just another Q&A site. Although technically correct, due to our rules and organization we're a lot more than that. Right now it's possible to find answers to most, if not all, beginner questions. We've become one of the, if not best, programmers resource. The problem is that by giving the 'Ask Question'-flow dominant care and placement we're actually motivating new users to ask their questions rather than search for answers. This is a direct consequence of the structure and setup of the site, not of "lazy newcomers" or "help vampires" and can be solved by giving the search flow far more dominant placement and care (see mockups below) specifically for very low rep and guest users.

After reading through various discussions regarding the problem of 'help vampires' (users that simply ask questions, doing nearly no troubleshooting of their own and not contributing back the community). Although I do not believe they are that big of a problem on their own, I do agree that it's a bit sad how right now 3 out of 4 questions I see on the homepage that are asked by users with rep under 50 are answerable using a simple Google search limited to StackOverflow questions (and the fourth could be answered by combining two other questions).

We already have the content, and yet we spend a lot of time and effort closing and answering the same questions over and over and over again. Now, rather than just complaining I was thinking how one could possibly solve this issue and one thing that hit me is to make the Stack Overflow homepage a true search homepage with the search box up front and centre for very low rep (<15 or so) and new users. Additionally it would also be good to give the search bar a more dominant placing on the question pages, once again primarily or only for low rep or guest users. This would come along with hiding user interface elements such as 'Ask Question', 'Top Questions', 'Users', 'Badges', 'Unanswered' and maybe even the 'Hot Network Questions'.

So, just to make it clear I made a screenshot of the current homepage:

And what I am proposing would be something like this. Or in response to an answer by Sam one could add a link to the Q&A/Social homepage as well like such (which I believe is an excellent idea/point):

And only on the search results page or the Q&A homepage would the option be shown to ask your question. In previous versions of this question I wrote that I could not think of any situations where one could wish to ask a question as a new user without first searching. The interesting point has been made by Cerbrus that a user who has searched previously and then comes back to the site will have searched already and knows the answer is not on the site. A possible solution could be to show the button based on previous search habits which could be stored client side without an account. Now, personally I think the link to the Q&A homepage is more than enough, but this could definitely be something to consider.

Another point that has been raised is that a lot of new users don't access the SO page through the homepage (though those who come from Google are probably already a smaller 'problem'), so a redesign like this could be considered:

The Ask a Question option could definitely not be removed as the user likely already came from Google, however changing the priority of the UI elements could get a lot of users into the search flow first rather than the ask a question flow. Additionally showing the Q&A info banner might not be necessary any more which would clean up the design a lot as well.

Advantages

• New users will have consciously searched the site. It will not take a lot more work than the current Ask Question process, but it will be a two step process where instead of in a small box inside the form the similar questions are shown full size.

• For a lot of established languages all simple questions have been asked already. This is something I have been realizing more and more lately, but it is kind of true. New users tend to have questions about established languages rather than exotic libraries or languages, so improving the search experience should be more important than improving the 'ask a question' and 'moderation' processes.

Disadvantage

• The current search engine is far from good. It would either need rebuilding or for example one could try contacting Google whether they'd like to support StackOverflow with 'Google Search for Enterprises'. This discussion is out of scope for this feature request/proposal and there are other questions discussing various aspects of the search engine and presentation.

So, yeah, just an idea I had, looking forward to seeing your opinions.