My experience with Norton products is that in the
unlikely event they find an issue, they self-destruct if they manage to remove it...
OK, what is the directory (File path, like C
Windows/System 32/Virus_is_here.exe) that the Virus resides in?
Download Abexo Free registory scanner from download.com, as you'll be needing it for a manual removal. Also, get onto a realy old Windows 98/95 PC and format a new Floppy Disk. After that, put on DOS to the said floppy.
Try un-installing Norton 360 and installing AVG. If that doesn't get it, you'll have to do a manual removal. Two disclaimers;
Removing Norton products often kills the system on which they were installed. Removing a virus manually often kills the system it was on. AVG will remove it if it isn't active. If it is active, the PC will try to load the trogan as it loads. If it can't find the removed file as it loads and realises soon enough, 9 times out of 10, the system will blue screen of death you...
Back-up everything of importance to exturnal media before you go any further. If you try to access your files on said exturnal media on a different computer, virus scan the media and remove the virus that will likely have copied itself onto the media also if it was active before even trying to see the files on the disk. This avoids the virus spreading onto the other PC's. Check that you have the Manufacture's recovery CD's to hand also if you manually remove the virus. You are likely going to need them...
All the best
Rabbut