I've yet to find an infection so bad that I had to go nuclear. I did deal with an infection that sounded very much like this one, and it was indeed tough to get around, as the virus prevented you from running anything it didn't want to have running.......such as anything that might get rid of it. It was a renamed ComboFix that broke its stranglehold and let me get at it. Have you tried renaming it something totally stupid, like, ert-y76p.exe? Does it even attempt to run when clicked, or does it just sit there?
Another option that I have used on a number of severely virused-up machines is F-prot for Linux running off a LiveCD. Try downloading Puppy Linux 4.1.2, burn the image to a CD (must be done with the "burn image" function, not just burning the file,) and boot from it. If you can get it to connect to the internet, (90-95% odds you can, if only wired) then the XFProt item on the menu will download the very latest version of F-Prot, and give you a skin through which to look at the output. I don't recall if there's any way to tell it to automatically delete the junk it finds, but it gives you a nice detailed log of what it finds, so you can address the problems it finds any of a number of ways. Puppy Linux is great for stuff like this as it's a quick download and it's very easy to get it live.
If it comes down to it, is there another computer you could simply add your hard drive to as a second and simply scan it with Avast that way?