If it's a Dell computer, you can go to the Dell website and run their diagnostic program regardless of how old the computer is. It only works with IE though. I think HP also does the same thing. I know for a fact that Toshiba is very quick to end support for their older laptops.
Many computers come with diagnostics software on a separate partition nowadays. Of course, if the computer doesn't work then that could pose a problem. But if it does, or is repairable, you could use that for a test computer.
I use SeaTools for Windows to test hard drives. It's free. Also there is a free program called Speccy that you can install on any Windows XP, Vista, or 7 computer that gives you a lot of info about RAM, CPU, hard drive, etc. In some cases it reports the status as well.
A friend of mine who is a repair tech suggested PC Check. I looked into it, but that's not cheap either.
That's all I can think of as far as software. One of these days I want to have the guts to ask different repair techs how they test hardware.
Edit: As per the above post, I often use DBAN to wipe hard drives. If I only need to perform a lower level wipe, I use Linux to wipe them clean. Never stick them in a Windows OS based computer. Most viruses are written for the Windows OS and can't touch Linux. It is much safer to connect them to a computer run by a Linux OS and do a low level wipe first just in case. This way you don't have to constantly restart the computer if the hard drive doesn't work. Just make sure, in either instance, that you choose the correct hard drive to wipe. Believe me, I know.
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