POST SCRIPT:
So here it is almost six years later and the same thing happens, i.e., power outage and I neglect to remove the AC cord from the power supply. I knew I had had this issue before, so I researched the JRDG website. The manual seems to suggest that the unit can survive off battery power 15-18 hours, and since the power company was indicating a restoration time of about 7 hours, I decided not to remove the AC from the unit. When the power was restored, the unit powered up, but as before, the AC lamps did not illuminate, it neither read "LOW" or "FULL". So I'm thinking, here we go again, I killed another pair of batteries which I do not believe are even a year old. The reason I am writing is because this time, much to my pleasant surprise, the "FULL" lamp came on after about an hour of the AC being applied to the unit. This suggests to me that this time, my batteries were strong enough to survive this depletion whereas the earlier set must have been much older and weaker. So the take away for anyone experiencing this problem is that if after a few hours, neither your "LOW" or "FULL" lamps have illuminated, you need to replace the batteries. On the bright side, if the batteries did not withstand the depletion, they were probably due to fail soon anyway. I hope I can find this post in 5 years, the next time this happens and I am doomed to repeat my stupidity.