Virus, malware, spyware, trojans problems for sureeeee HELPPPP?

so I went away for a week, and my cousion needed the computer for a week and I clearly told her to use the other computer. We have two of them. She mistakenly used the one with the subscribed antivirus. Now I come home and she tells me there are some problems with the computer, like pop ups runs slower than normal and when I looked at it, these things do happen indeed. Also seems like third party sites claiming they can remove the viruses and what not advertisements appear. I know she visited some porn sites. I keep getting messages from the old norton antivirus that virus has been repaired (velara, downloader etc.) and some viruses cannnot be removed as norton says. I am going to the store tomorrow to get norton internet security 2008 because it is what I can get at a good price. I am in a personal need to fix this problem. I am also getting messages like advertisements which seem to say remote computer is tracking. and things are showing on the desktop acting like windows security an

Virus, malware, spyware, trojans problems for sureeeee HELPPPP?download

Whenever a piece of anti-malware reports something but can't seem to delete it, run it again in Safe Mode. Safe Mode often prevents the malware from running and protecting itself.

Also, turn off System Restore to evict any copies of bad stuff that might be lurking there.

To get into Safe Mode: