The other basic test that's advisable and easy to do: run Memtest 86+ to check your memory. It boots with its own OS from a cd or flash drive. The Ultimate Boot CD contains that and most every other freeware diagnostic. It's a free download and also needs to be burned to a cd or loaded to a bootable usb drive. Having a bootable disc like this or a live linux disc is useful as a basic diagnostic. Even if your hdd or ssd or OS is trashed you can tell if the rest of the hardware is okay. A good live linux disc will also get you online to get help, access email, etc.
That link at the bottom of Midknyte's post is to the Ultimate Boot CD.