Perhaps they go blank when you ask them to think because it's been so long since they've tried to think in math class. Sadly, many (most?) students just try to memorize procedures.
You'll need to find problems that suck them in, so they really want to think. Also, you'll need to give them some strategies for problem-solving. How to Solve It, by George Polya has lots of great ideas. (Here's an online copy of the one-page outline he devised.) You can also find some excellent material at Avery Pickford's blog, by searching on "habits of mind."
Brainstorming helps, which means working in groups is much more effective than working solo. But it takes a lot of savvy to facilitate good groupwork. One principle for what types of problems are best used in this situation is that they have multiple solution paths, and a somewhat open answer. This sort of problem is often called a "rich task."
If you're teaching high school, there has been work done on "complex instruction," which refers to a suite of strategies used to get students thinking, while using lots of groupwork. I've found this work useful, although I am not comfortable using all their strategies with my college students.
One more note on your students' responses to your attempts so far: Students have taken math for many years by the time they reach you, and have expectations of math class. When you violate their expectations, there will be pushback. According to James Stigler, author of The Teaching Gap, much of it is deeply imprinted in us, as what school is. He writes, “The scripts for teaching in each country appear to rest on a relatively small and tacit set of core beliefs about the nature of the subject, about how students learn, and about the role that a teacher should play in the classroom.”