I know several people personally who are non-technical, and have successfully built and sold technology businesses. Sure, they had to put money in them, but they did "succeed". The point is, those startups were within their reach, because they had the funds and management knowledge to make them happen.
I am not at liberty to disclose who those companies are, however. Some, I've signed NDAs with, and others I haven't asked them if I could disclose that they used subcontractors.
Worth adding that I was the first to be surprised that they managed it. I don't believe in outsourcing your core business processes. However, whether or not I believe it, they did it.
I'm not actually advocating this as a standard model, btw. I think if you're not technical, you should start a business that doesn't require lots of technical knowledge. There are plenty of those opportunities out there.
Groupon is an example of a huge technology business that didn't require all that much technical skill to get off the ground.