How do I fix my computer suddenly running slowly?

Yesterday, I was using one of my school's wireless connection surfing the web on facebook, blackboard, and a (frequently visited) wiki website and my internet explorer stopped responding. This was nothing unusual at first, so I just pressed ctrl+alt+del and clicked on task manager. Task manager took forever and a day to come up, my screen almost looked frozen suddenly. The performance was unbearable, so I just cut it off and turned it back on only to stare at Welcome with a loading icon next to it for like 20 minutes. I cut it off again and went to safe mode which was still slow, but not as slow and tried to scan my computer then cleaned up my registry. After that I did Disk Cleanup and Disk Defragmenter and my computer started running a little faster, but it's still slower than it was yesterday and all the time before that. The startup varies from kind of slow to go-watch-tv slow, and isn't slow at all in safe mode. Also, during my scan I saw some backdoor.rustock files and some other backdoor files, but my norton didn't identify it as a threat.