Hi everyone, thank you for the replies! I've been really busy recently and I forgot that I had posted here for help.
swifty_morgan, as is obvious, I am still connected to the Internet, so this isn't the same virus.
Branden, the program that you linked to did not report any issues with my DNS.
I didn't mention this earlier because I didn't entirely understand what was going on, but Windows Firewall is also broken; trying to "Use default settings" does nothing, and there are also some errors with the associated Services.
I'm gonna just do a repair install as suggested on another forum, here in a couple of days. Thank you all for your help!
DNS has nothing to do with your connection to the internet. Without DNS you cannot resolve names to IP addresses but direct IP connections will still work