The machine has issues you need to resolve before considering SP2. SP2 is a two edged sword. It does contain many security fixes, but pre-existing conditions can transform a machine to a doorstop.
All I can offer is that you should eject all SPYWARE with Adaware, Spybot, Stinger and Hosuecall as well as read the Shutdown article for XP at http://www.aumha.org/articles.htm
My wife's HP computer with one 256 RAM chip gives a "Memory Parity Error" & blue screen when I attempt to shut it down and requires that I physically shut it down by pressing the power key. Wouldn't memory parity suggest a conflict between *2* RAM chips? She only has *1* RAM chip. It is also refusing any windows updates - including XP Service Pack 2. I've tried using the SP2 CD I ordered from Microsoft and that has failed as well. The computer will uncompress the files correctly, but when it comes time to run the Service Pack (or any other Windows Update) executable file nothing happens. Any suggestions? Thank you in advance for your help! This one has me stumped!