I have had this EXACT thing happen to me a while back. It was the same Svchost virus.
I had it and none of my virus caners would pick it up but I found out what was wrong with it. Useally the Svchost.exe is located in a windows system file. What I found out was that this one was located in my temp folder.
I downloaded Hijack This!
Scan the computer, You can put this on a flash drive and run it on the computer from there; since you can't get websites to load.
After you scan it, Save the file, and put it on the flash drive again and go to this site:
Load the file into that site and it should come up with a list of the programs that are running in the background. It should have an X in red on the right if it's bad.
If you want to skip some of that, just check if the svchost.exe in HijackThis is in a different folder other than a Win32 folder. If it is, just simply check it and hit fix.