Thanks for the suggestion, timmcat, but unfortunately, it hasn't helped. I started up with minimum programs using Startup Cop, with AVG, Counterspy and Zone Alarm all off. Installed - no joy. Plugged in the IPOD - got the 'do not disconnect' message for about three minutes. However, iTunes did/would not open and I did not lose the songs already on the IPOD, which would suggest that it didn't find the empty My Music/iTunes library on the computer.
iTunes starts up fine on my second computer, but unfortunately, it has a hard drive too small to accommodate the audio files.