Well, rumbling with torrent sites is actually a death game. I've done it somewhat myself, and nothing good came out of it in the - pretty much like patcooke states. Fun for a start, pure pain in the end.
If your computer is infected, and that sounds likely, a new Internet connection will not correct the situation. You see, the persistent bugs are on your hard disk, and there they stay.
I would suggest a thorough scan, preferably also with an on-line scan, to get a second view. The only definite way to get rid of infections is a zero format + re-installation = resulting in a clear disk with a new installation. But if your computer works, scans + cleaning may work.
But anyway, and this you should understand by own experience: stay out from torrent places.