With over 7 billion people out there, certainly there is someone who can fill the position you are hiring for. Of course they do not all live in North America, or the UK, etc. but when you put out the giant sifter, you should be able to isolate a few choice people.
Here are some articles on how other companies do it and/or explanations about why your process is not working:
1. Here are Google, Amazon and Facebook’s Secrets to Hiring the Best People
2. An article from Workopolis on three reasons why smart people don’t get hired
3. An article by Jeff Atwood, Founder of Stack Exchange and Discourse, on why you are not hiring the best and the brightest
4. An explanation about why Steve Jobs considered hiring the right people your most important job and how to improve your hiring skills
5. An article on Careerswiki outlining the enormous role social media plays in both sourcing candidates and finding jobs
6. A Talentlyft outline of 8 recruitment strategies to attract the best talent
Hope some or all of these work for you !!!