Hey Aleksander!
Taking down the net is tricky as the original purpose of the Internet is to keep computers up and running in case of any sort of disaster. However, there are ways to disrupt the net and sections of the Internet. It would be helpful to know why they are trying to destroy the net (kill people's access to information? Take over the sources of information? throw everyone back to the age before computers?) and to know what sort of computer power this fringe group would have access to (have they built a super computer of slave computer? do they have access to a supercomputer?). However, even without all those details there are a few things ranging from low tech (power surges take down nodes) to cutting or damaging underwater cables like the 2008 disruptions (see
http://en.wikipedia.org/wiki/2008_submarine_cable_disruption) to really high tech like the Stuxnet worm (see
http://www.cnn.com/2012/07/10/tech/web/internet-down-eagleman/) or a virus, which you've already got, that could really cause some disruptions.
Also, you might find this fun and/or helpful:
http://www.outageanalyzer.com This site tracks internet outages in real time. Not sure if your protag could use this or not, but thought I'd throw it in there.
I'm not sure if any of this is really helpful, but hopefully it will at least spark an idea for you!
Although, now that I've thought about it, being a little vague is probably a good idea since all of this sort of thing can change so quickly. There is an adult thriller writer who is also a Microsoft employee --so sorry, can't think of his name right now -- who writes computer security thrillers. You might want to check out one of his books to see how he handles the technical aspects (he's got real terms and plausible scenarios but is a little vague about the exact ways that things happen). If I think of it in a minute I'll add it...
Good luck! Sounds like a fun story!