What you saw isn't unusual at all; I used to see it on black-and-white TVs/monitors all the time 20 years ago. (For some reason color monitors seem more immune to it, or at least the symptoms tend to be more subtle.) The line is a burst of interference from the ballast of the fluorescent lamp hitting the monitor every 1/60th of a second, and it moves vertically across the screen because the line frequency of the utility's AC power isn't *quite* in sync with the screen refresh frequency of your monitor. As Trash notes you could get the same thing from setting two poorly shielded CRT monitors close to each other; in that case the interference is usually from close-but-still-mismatched vertical sync pulses.
This used to be a serious problem in offices that had the old eye-killing 60hz florescent ballasts. Most buildings use higher frequency ballasts these days but you still find the old-fashioned ones in small desk and utility lamps.