Shutting off the wireless connection would stop it but scanning with Norton, either in normal or safe mode, turned up nothing. I also installed Spybot S&D and scanned, but still no luck. I thought that the Norton AV application "DoScan.exe" might be infected or a trojan because there was a bigger copy in the prefetch area than the real one, so I deleted it. I also thought I got it, but it still was infected.
I finally had to give up for the day and come back. I thought Norton might actually be infected so I was going to go back and install AVG to see if it could have better luck. This morning I woke up thinking about something I had heard about on a "Security Now" podcast; rootkits. Designed to hide files and registry entries from the operating system, they can also hide from scanners who rely on the OS to show them the files to be scanned. They can also be detected by comparing the OS results to data read and parsed from a BIOS level read of the HDD.
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A final scan by Rootkit Revealer showed no hidden files or registry entries. When the network connection was turned back on and the system rebooted, no sign of any infection. Ta Da!
Update: Had my second today. I was a lot quicker on the uptake this time.