My viruses getting virus

Sorry for not being available, but I decided to reformat my harddrive. No big deal, hardly something that would leave me without web for more than a couple of hours...or so I thought. You see, my current line of protection consists of Norton 2003 and Zone Alarm. The first needs virus definitions and the other needs to be downloaded from the web. In the 5 minutes it took me from the time I had internet again and till I had gotten both, I had gotten a grand total of 3 viruses. One of them infected in the other, and the last giving me a grand total of 60 seconds to do anything before a restart ^_^
But I had Norton! I could just get rid of them all! Ehh...nope! When a virus has infected another virus, they apparently become somewhat harder to remove. Actually, a whole lot harder to remove. And don't even think about identifying them all. After a lot of bickering and rebooting in various modes and formatting my computer (grand total of 4 times), I had to give up and wait til I could get my mp3 player to another computer where I could download zone alarm and a fresh pair of virus defs. Meh! Bloody crackers....