Obviously
memtest86 for your RAM testing, although you'll need to burn it to disk/floppy in order to use it. You can also check by HDD manufacturer's websites and see if they have programs to download for free. I know
Hitachi has one, as does
Seagate. These will also have to be burned to a CD to work, but that's going to be typical of many hardware scanning programs out there. There is a program called PC-Check that can test all major components of a computer, but since it's a corporate utility, there isn't a download for it to my knowledge.
Software wise, these will do fine for virus and malware removal, plus maintenance and general cleaning:
Trojanhunter,
NOD32,
Ad-Aware,
Spyware Doctor,
Ewido,
Ccleaner,
Registry Mechanic, and
Diskeeper. These programs, along with whatever hardware diagnostic tools you can find, should allow you to handle most problems that will crop up with your average computer.
Jam it back in, in the dark.
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Sol