When your system freezes there is nothing you can do to analyze the situation. Usually, you won't even be able to do any post-mortem analysis, because no information about the hang is recorded.
The method described in the article you linked is intended to be used by driver developers that have to cause a crash for testing purposes. It would not have helped you in your situation, primarily because you didn't have the registry key set when it happened. If you had it set, you could have caused a crash and would have a memory dump for post-mortem analysis.
What could I do with it?
Probably nothing. When you collected such a dump through a regular crash, it would usually contain easily obtainable information regarding who or what caused the crash. You can get that information by loading the dump into windbg and executing:
However, if you had enabled the registry option to cause a crash, windbg would indicate that the keyboard driver caused the bug check.
You could check the other processes and threads that were recorded in the dump to find what actually caused the hang. But you should really know what you're doing and/or looking for.
So, what should I do?
The problem with random hangs is that they're random. As long as they appear random, there's nothing you can do. You can observe the behavior long enough until it doesn't appear random anymore.
Once you realize that the problem happens due to a certain pattern, you can start troubleshooting the issue.