hey merlin, if she has had the computer for a while, there is for sure a bunch of crap in the registry that is slowing the computer way down. there are also probably a ton of bad shortcuts and other stuff that generally compound and can slow those things down like crazy. sometimes it's not all adware/malware, etc that slow down a system. there are some good programs like norton utilities and system mechanic that work pretty well at cleaning out the bad files. also, try downloading and running CWShredder. there is most likely some "cool web search" stuff on her computer, especially if spybot found so many things.
i've had great results with system mechanic on my parents computers. they are still on dialup and one of their computers had like 10 dialers on it that kept putting these crazy charges on their phone bill. i cleaned all those out and then did a full defrag and now the old 300 mhz pentium laptop is pretty quick again even running windows xp. i have no idea who decided to load xp on that old computer but i guess it works.
i think what a lot of people do when their computer starts slowing down a lot and they don't know what to do is to just go to compusa or whatever and buy a new one. everyone is always saying that any computer over a year or 2 old is outdated, but to be honest, if you're not an enthusiast or hardcore gamer you could probably get away with doing most everything on a PIII under 1ghz right now with no problems, as long as it's maintained.
oh, one more thing. i don't know if anyone mentioned pcpitstop.com yet, but that's a great starting place to check for shortcomings with the computer. also, you don't have to buy any software to make your computer work better. there is always a free trial or freeware version to clean it, so don't fork over cash for some program that claims it's better because you have to pay upfront. there is a reason over 66 million people have downloaded adaware from download.com.
ok, now go make grandma proud of you.