I had a 6100/66 with a dead battery for ages, the only thing it hurt was the clock settings. The thing seemed to always start up with no video. What I would do, even though this isn't prob the best idea, is turn on the switch til u hear the chime, then turn it off, then back on again and then the chime and video comes up. Worked for me for a while.
edit:
I did replace the battery eventually, don't recall if it helped the video at startup or not.. but I did get it from OWC for a few bux.