For the most part yes, a game should tell you if it's stable or not.
However, I have played NFSU for many hours, then tried prime95 for 5 minutes and crashed.
There are different tests for different hardwares.
Programs liek super_pi and prime95 are mainly CPU testers (memory testers too, but not majorly)
programs like 3dmark** are mainly video card and memory testers, but mainly heavy on the vid card.
You can look into a free software called "Sisoft Sandra" that has a pecific test for almost all hardware components, down to you NIC. Get the newest free version if you wish.
You can download and install 3DMark and jsut run it, no fancy installs or registering that i can remember.
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Compaq Presario V5000 laptop