What is the budget for this kind of project?
The money question is my favorite because we can solve anything -- if the client actually wants to pay for it. If the solution is far more expensive than the problem that they currently have, they're not going to buy the solution. You discuss budgets with the client because you want to understand more about the "why" of the project.
Consider the YouTube example. I can take an employee's salary, find out how much time they're spending on YouTube, and then calculate exactly what YouTube "costs" that client. And if my solution for blocking and managing YouTube activity is cheaper than that, I'm offering cost savings. Otherwise, it doesn't necessarily make sense for them to solve that problem. It's about the value proposition of the project.