I am looking for hints, tips and answers on how to get started on troubleshooting when:

1. The problem is intermittent
2. The problem could lie literally anywhere - operating system; free source software; my own software developments; purchased software; crumbs on the keyboard; the specific combination of software I am currently running; Maxwell's demon; the little blue men actually running the machine have gone on strike; etc.
3. I have expertise only in a few of the areas that are potential candidates for the cause of the problem.

The specific problem I am having is detailed below as an example, but I am not seeking answers to my current problem, but rather where and how to start on tackling such problems.

I am currently encountering a problem with my new machine. On a few occasions the machine has just frozen; not accepting keystrokes, mouseclicks, or anything except the power on/off switch. Invariably I have been merely browsing the web; I have had a few (<= 6 other applications) running. None of these applications are major; and represent a mix of commercial programs and open source programs, typically migrated from Unix of some variety.

My machine is a Windows 7 I7 quad core laptop.