The spyware/trojan horse angle sounds the most likely cause.
I cleaned up a friends computer and their son's computer a couple of weeks ago - both were infected with multiple viruses and multiple trojan horses.
Two weeks later and their son's computer is again grinding to a halt. Took a look at it this weekend for them while I was there for a party and sure enough it was once again loaded with multiple trojan horses.
He's hooked on downloading JPEGs, MP3s, games, etc. from a number of sites that he and all his high school friends frequent - but the sites require the use of special download and (in some cases) play software which are loaded with spyware, viruses, and/or trojan horses/backdoors.
Told his parents that I could clean his PC again, but unless he's going to stop downloading all that crap he'd be reinfected in less than a week.
Just in case, I'd already isolated his computer from the rest of the home LAN when I set it up for them so things on his computer couldn't reach out and mess with their other computers.
On the Windows Task Manager's Process tab, with nothing else running on the computer, look for processes that continue to use CPU. Note the process names. They could be getting started from the Startup folder or through Registry entries. You may also have to search using Find Files for their names in files in case they're using a launch redirection ploy.
Good luck.