I would probably use a burn-in / stress-test / benchmark program, and run it for as long as possible. Failed hardware might not always make itself known when it's idle, so firing it up to full speed is a good way to tell if the hardware is functioning properly, because that's usually the time it will complain (crash).
Prime95 (CPU), MemTest86 (Memory), and 3DMark (Video) are probably the standard applications that most geeks here use for extreme stability testing. A good how-to article (though a little outdated) is available here:
Guidelines for Thorough Stability Testing - Overclockers Forums
For small benchmarks and analysis, you could just use an all-in-one program called PCWizard 2008. It's not great for stress-testing, but it is good for hardware analysis and getting system info. You can download it here:
Have fun with your new notebook!